### Talks in 2015

#### Vorstellungsvortrag

**Title:**Über Automaten-Gruppen

**Speaker:**Dr. Daniele D'Angeli (Institut für Mathematische Strukturtheorie)

**Date:**18.12. 11:30

**Room:**Seminarraum Geometrie

**Abstract:**

In diesem Vortrag möchte ich eine grundlegende Präsentation der

Theorie der Automatengruppen, auf die meine Forschung

sich größenteils konzentriert, halten. Ich werde eine historische

Einleitung, die grundlegenden Definitionen und die Motivationen,

die überzeugen sollen, warum es interessant ist, solche Gruppen zu

studieren, diskutieren. In dem zweiten Teil des Vortrags

werde ich einige Forschungsergebnisse, die ich in den letzten Jahren

im Kontext der Automatengruppen bekommen habe, und

mögliche Forschungsprobleme, die ich in der Zukunft behandlen möchte, zeigen.

#### Vorstellungsvortrag

**Title:**Asymptotic Entropy of Random Walks on Regular Languages

**Speaker:**Dr. Lorenz Gilch (Institut für Mathematische Strukturtheorie)

**Date:**18.12. 10:15

**Room:**Seminarraum Geometrie

**Abstract:**

In this talk I will consider transient random walks on an infinite set

of finite words over a finite alphabet. These random walks are of

interest in an information-theoretic context; important results in this

field have been achieved by S. Lalley and V. Malyshev.

We are interested in the asymptotic entropy, which is a characteristic

invariant of transient random walks measuring the asymptotic amount of

information or uncertainty contained in the random word at time n. While

existence of the asymptotic entropy of random walks on groups is

well-known, existence for random walks on other structures is not known

a priori.

The purpose of this talk is to give a short introduction to entropy, to

present the ideas of my existence proof of asymptotic entropy for random

walks on regular languages and to prove the real-analytic behaviour of

the entropy in terms of probability measures of constant support. The

methods used in my work comprise generating function techniques and the

concept of cones in graphs, which allow to cut the random walk

into pieces such that this sequence of pieces form a hidden Markov chain.

#### Algebra Kolloquium

**Title:**Polynomial functions over residue class rings of the integers

**Speaker:**Ashwin Guha (Indian Institute of Science, Bangalore)

**Date:**Donnerstag, 17. 12. 2015, 16:00 s.t.

**Room:**SR A206, Geodäsie, Steyrergasse 30/2.St.

**Abstract:**

Abstract:

Polynomials and their induced functions over finite fields have been

well-studied. The literature on polynomial functions over finite

commutative rings is considerably smaller. In this talk I will

provide a description of polynomial functions over a specific instance of

finite commutative rings, namely, set of residue classes of integers. This

characterization obtained by considering the set of polynomial

functions as a module and providing a set of generators for it is

particularly useful for computational purposes.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**The core in random hypergraphs and local weak convergence

**Speaker:**Kathrin Skubch (Goethe-Universität Frankfurt)

**Date:**Dienstag 15.12.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

\noindent The degree of a vertex in a hypergraph is defined as the number of edges incident to it.

In this talk we study the $k$-core, defined as the maximal induced subhypergraph of minimum degree at least $k$, of the random $r$-uniform hypergraph $\mathbf{H}_r(n,p)$ for $r\geq 3$.

We consider the case $k\geq 2$ and $p=d/n^{r-1}$ for which every vertex has fixed average degree $d>0$. We derive a multi-type branching process

that describes the local structure of the $k$-core together with the mantle, i.e. the vertices outside the core.

#### Advanced Topics Seminar

**Title:**Maximal Persistence

**Speaker:**Primož Škraba (Univerza v Ljubljani, Slowenien)

**Date:**Freitag, 11.12.2015, 10:30 Uhr

**Room:**Seminarraum 2 (Geometrie), 4. Stock, Kopernikusgasse 24

**Abstract:**

Persistent homology is a central tool in topological data analysis. It describes various structures such as components, holes, voids, etc. via a barcode (or a persistence diagram), with longer bars representing ``real'' structure and shorter bars representing ``noise.'' A natural question is how long are the bars we can expect to see from data with no structure, i.e. noise. In this talk, I will introduce some recent results regarding the persistent homology of random processes, specifically, a homogeneous Poisson process. Only an understanding of basic probability will be assumed, with the required topological and probabilistic methods introduced as needed.

#### Zahlentheoretisches Kolloquium

**Title:**Problems with packing periodicity

**Speaker:**Dr. Wöden Kusner (TU Graz)

**Date:**Freitag, 11. 12. 2015, 14:00 Uhr, s.t.

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

When we think about packing problems, our intuition often leads us to

believe that the solutions should exhibit some exceptional

symmetry. I'll survey some interesting problems and examples dealing

with packing and periodicity, particularly some that break more symmetry

than you might think.

In this context, I'll also tell you about recent joint work on packings

of a generic polygon in the plane: By introducing a useful topology on

packings and describing the local optimality of a configuration among

double lattices as a consequence of an algorithm of Mount, linear

programming techniques can often certify the best double lattice packing

as a local maximum for volume fraction among all packings.

#### Kolloquium: Mathematische Methoden in den Natur- und Ingenieurwissenschaften

**Title:**Space-time Trefftz discontinuous Galerkin methods for wave problems

**Speaker:**Univ.-Prof., PhD Ilaria PERUGIA (Universität Wien)

**Date:**Mittwoch, 9.12.2015, 11:30 Uhr

**Room:**TU Graz, Steyrergasse 30, 3. Stock, Seminarraum C307

**Abstract:**

#### Advanced Topics Seminar

**Title:**Semidiscrete surfaces with constant mean curvature and their associated families

**Speaker:**Wolfgang Carl (TU Graz)

**Date:**Freitag, 4.12.2015, 10:30 Uhr

**Room:**Seminarraum 2 (Geometrie), 4. Stock, Kopernikusgasse 24

**Abstract:**

#### Gastvortrag

**Title:**Stable invariants for multidimensional persistence

**Speaker:**Martina Scolamiero (EPFL - Laboratory for Topology and Neuroscience)

**Date:**4.12.2015, 13:00 (ca. 45 min)

**Room:**Seminarraum 2, Kopernikusgasse 24, 4. Stock

**Abstract:**

Multidimensional Persistence is a method in topological data analysis

which allows to study several properties of a dataset contemporarily. It

is important to identify discrete invariants for multidimensional

persistence in order to compare properties of different datasets.

Furthermore such invariants should be stable, i.e., data sets which are

considered to be close should give close values of the invariant.

We introduce a framework that allows to compute a new class of stable

discrete invariants for multidimensional persistence. In doing this, we

generalize the notion of interleaving topology on multi-dimensional

persistence modules and consequently the notion of closeness for

datasets. A filter function is usually chosen to highlight properties we

want to examine from a dataset. Similarly, our new topology allows some

features of datasets to be considered as noise.

#### Zahlentheoretisches Kolloquium

**Title:**Polynomial overrings of Int($\mathbb{Z}$)

**Speaker:**J.-L. Chabert (LAMFA, Universit\'e de Picardie, Amiens)

**Date:**Donnerstag, 3. 12. 2015, 16:00 (s.t.)

**Room:**SR A206, Geodäsie, Steyrergasse 30/2.St.

**Abstract:**

Abstract: We show that every polynomial overring of Int($\mathbb{Z}$), the ring of

integer-valued polynomials over $\mathbb{Z}$, may be

considered as the ring of integer-valued polynomials over some subset of

$\hat{\mathbb{Z}}$, the profinite completion of $\mathbb{Z}$ with respect to

the fundamental system of neighbourhoods of 0 consisting of all non-zero

ideals of $\mathbb{Z}$.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Bootstrap percolation in $G(n,p)$

**Speaker:**Tamas Makai (TU Graz)

**Date:**Dienstag 1.12.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

Bootstrap percolation on a graph $G = G(V;E)$ with activation threshold an integer $r \geq 1$ is a deterministic process which evolves in rounds. Every vertex is in one of two possible states: it is either infected or uninfected.

The set of initially infected vertices is given by $\mathcal{A}(0)$. In each round of the process every uninfected vertex $v$ which has at least $r$ infected neighbours becomes infected. Once a vertex has become infected it remains infected forever. The process stops once no more vertices become infected.

We consider the case when the graph $G$ is a binomial random graph and $\mathcal{A}(0)$ consists of a given number of vertices chosen uniformly at random.

Janson, {\L}uczak, Turova and Vallier (2012) determined a threshold $a_c$ such that for any $\omega(n)\gg \sqrt{a_c}$ if $|\mathcal{A}(0)|<a_c-\omega(n)$ then w.h.p.\ only a few additional vertices become infected. However if $|\mathcal{A}(0)|>a_c+\omega(n)$ then almost every vertex becomes infected. We show that this not only holds with high probability but with probability $1-\exp(-\Omega(\omega^2/a_c))$.

This talk is based on joint work with Mihyun Kang.

**Title:**Zahlentheoretisches Kolloquium

**Speaker:**()

**Date:**Donnerstag, 26.11.2015 und Freitag, 27.11.2015

**Room:**26.11.: SR A206 Geodäsie, Steyrerg.30/2.St., 27.11.:SR 2 Geometrie, Kopernikusg.24/4.St., SR C208, Mathematik, Steyrerg.30/2.St.

**Abstract:**

Donnerstag: 26. 11. 2015, SR A206, Geodäsie, Steyrergasse 30/2.St.

16:15: **Martin Widmer**, (Royal Holloway Univ. of London, dzt. TU Graz)

*Around the Northcott Property - Many new problems and some new results*

17:00: **Christopher Frei**, (TU Graz)

*The Hasse norm principle for Abelian extensions*

17:45: **Dijana Kreso**, (TU Graz)

*On common values of lacunary polynomials at integer points*

Freitag: 27. 11. 2015, SR 2, Geometrie, Kopernikusgasse 24/4.St.

10:30: **Alina Ostafe**, (UNSW, Sydney)

*On some extensions of the Ailon-Rudnick Theorem*

11:15: **Arne Winterhof**, (RICAM Linz)

*Pseudorandom sequences: measures and number-theoretic constructions*

SR C208, Mathematik, Steyrergasse 30/2.St.

14:15: **Fabrizio Barroero**, (Scuola Normale Superiore di Pisa)

*Unlikely intersections in certain families of abelian varieties and the polynomial Pell equation*

15:00: **Volker Ziegler**, (Univ. Salzburg)

*On the number of integers that are the sum of k units*

15:45: **Clemens Fuchs**, (Univ. Salzburg)

*On a family of quartic Thue equations over function fields*

#### Zahlentheoretisches Kolloquium

**Title:**Intersection of polynomial orbits over finite fields

**Speaker:**Dr. Alina Ostafe (UNSW, Sydney)

**Date:**Mittwoch, 25. 11. 2015, 14:15 Uhr

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

Abstract:

Motivated by results on intersections of orbits of D. Ghioca, T. J. Tucker, and M. E. Zieve in characteristic zero, we answer several natural questions about reductions of orbits modulo primes of polynomial dynamical systems defined over $\mathbb Z$. In particular, under certain restrictions, we give bounds for the frequency of the points in an orbit of the reduction modulo a prime $p$ of an algebraic dynamical system that belong to a given algebraic variety. Our approach is based on recent explicit versions of Hilbert's Nullstellensatz and a new result about the reduction modulo prime numbers of systems of multivariate polynomials over the integers.

Moreover, we establish some links between these problems and the uniform dynamical Mordell-Lang conjecture. In this sense we present some upper bounds on the size of the intersection of an orbit in an algebraic dynamical system with a hypersurface for various cases when it is finite.

#### Strukturtheorie-Seminar

**Title:**Spectra of BBS automata

**Speaker:**Andrzej Żuk (Université Paris 7 )

**Date:**Freitag, 20.11.2015, 14 Uhr c.t.

**Room:**SR C208, Steyrerg. 30/III

**Abstract:**

#### Vorstellungsvortrag

**Title:**Optimales Investment für Versicherer

**Speaker:**Dr. Stefan Thonhauser (TU Graz)

**Date:**Donnerstag, 19. 11. 2015, 11:00 Uhr

**Room:**Seminarraum A306, Geodäsie,

**Abstract:**

Kurzinhalt:

In diesem Vortrag möchte ich auf ein Investmentproblem aus der Sicht

eines Versicherers eingehen. Im Gegensatz zu ähnlichen Problemen aus der

Portfoliooptimierung für welche die Wahl einer Investmentstrategie auf

Profitmaximierung ausgerichtet ist, soll in diesem Fall das Gesamtrisiko

reduziert werden.

Ich möchte dabei vorstellen wie sich die Einführung von

Transaktionskosten auf diese Fragestellung auswirken. Hier bedeuten

Transaktionskosten, Kosten welche bei jeder Adaptierung der Strategie

zusätzlich anfallen. Dieser Punkt ist zwar sehr realistisch, wird aber

in den klassischen Arbeiten zu diesem Thema vernachlässigt. Aus

mathematischer Sicht handelt es sich dabei um ein stochastisches

Impuls-Kontrollproblem dessen Lösung durch iteriertes optimales Stoppen

oder mittels der sogenannten quasi Variations-Ungleichungen

charakterisiert werden kann.

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Asymptotics for solutions of second order ODE's in a complex domain

**Speaker:**Philipp Schmitz (TU Ilmenau)

**Date:**26.11.2015, 15:00 Uhr

**Room:**C307

**Abstract:**

Motivated by non-Hermitian quantum mechanics (for example $\mathcal{PT}$ symmetric problems) second order linear differential equations in complex domains were studied over the last years. In particular, one is interested in $L^2$-solutions which correspond to eigenvalues of some associated operator.

In this talk the so called WKB approximation is introduced, which describes the asymptomatical behaviour for solutions of these differential equations. For a class of problems in $\mathcal{PT}$ symmetric quantum theory specific solutions are constructed by means of the WKB method. These solutions decay exponentially or diverge exponentially in certain areas of the complex plane, called Stokes wedges.

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Eigenvalue estimates for operators with finitely many negative squares

**Speaker:**Prof. Dr. Carsten Trunk (TU Ilmenau)

**Date:**26.11.2015, 14:00 Uhr

**Room:**C307

**Abstract:**

Let $A, B$ be selfadjoint operators with resolvent difference of rank one. Then the continuous spectra of the two operators coincide. The number of eigenvalues in a gap of the continuous spectrum is the same or it differs by one. This is a well-known fact for selfadjoint operators in Hilbert spaces.

The same question for selfadjoint operators in Krein spaces is more delicate. It arises naturally in the study of singular indefinite Sturm-Liouville problems which correspond to selfadjoint operators in Krein spaces. Often, a one dimensional perturbation leads to the direct sum of two (somehow 'decoupled') selfadjoint operators in $L^2$-Hilbert spaces} with well-known spectra. As a consequence, such an approach can be utilized to describe the spectrum of the singular indefinite Sturm-Liouville operator. As the continuous spectra of the indefinite Sturm-Liouville operator and its perturbation coincide, it remains to study the point spectrum.

Via the Weyl function, eigenvalue estimates in gaps of the continuous spectrum can be obtained: If the unperturbed operator belongs to one of the well studied

subclasses of selfadjoint operators in Krein spaces like operators with finitely many negative operators, then this is reflected in the properties of the Weyl function which we use to prove eigenvalue estimates. We emphasize that these estimates are sharp.

This is a joint work with J.\ Behrndt (Graz) and R.\ Moews (Berlin).

**Title:**Zahlentheoretisches Kolloquium

**Speaker:**Sigrid Grepstad (JKU Linz) Adrian Scheerer (TU Graz) ()

**Date:**Mittwoch, 18. 11. 2015, ab 14:15 Uhr

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

14:15: Sigrid Grepstad

*Sets of bounded discrepancy for multi-dimensional irrational rotation*

15:00: Adrian Scheerer

*Algorithms for Absolutely Normal Numbers and Discrepancies*

#### Vortrag

**Title:**Recent advances in Bayesian spatial prediction and sampling design

**Speaker:**Jürgen PILZ (Institute of Statistics, University of Klagenfurt)

**Date:**27. November 2015, 14:30 h

**Room:**SR für Statistik (NT03098), Kopernikusgasse 24/III

**Abstract:**

Abstract:

In my talk, I will report on recent work with my colleagues G. Spoeck and H. Kazianka in the area of Bayesian spatial prediction and design [1]-[5].

The Bayesian approach not only offers more flexibility in modeling but also allows us to deal with uncertain distribution parameters, and it leads to more realistic estimates for the predicted variances. We report on some experiences gained with our approach during a European project on "Automatic mapping of radioactivity in case of emergency".

We then go on and apply copula methodology to Bayesian spatial modeling and derive predictive distributions. Moreover, I report on recent results on finding objective priors for the crucial nugget and range parameters of the widely used Matern-family of covariance functions.

Furtheron, I briefly consider the challenges in stepping from the purely spatial setting to spatio-temporal modeling and prediction.

Finally, I will consider the problem of choosing an "optimal" spatial design, i.e. finding an optimal spatial configuration of the observation sites minimizing the total mean squared error of prediction over an area of interest. Using Bessel-sine/cosine- expansions for random fields we arrive at a design problem which is equivalent to finding optimal Bayes designs for linear regression models with uncorrelated errors, for which powerful methods and algorithms from convex optimization theory are available. I will also indicate problems and challenges with optimal Bayesian design when dealing with more complex design criteria such as minimizing the averaged expected lengths of predictive intervals over the area of interest.

References:

[1] H. Kazianka and J. Pilz: Bayesian spatial modeling and interpolation using copulas. Computers & Geosciences 37(3): 310-319, 2011

[2] H. Kazianka and J. Pilz: Objective Bayesian analysis of spatial data taking account of nugget and range parameters. The Canadian Journal of Statistics 40(2): 304-327, 2012

[3] J. Pilz, H. Kazianka and G. Spoeck: Some advances in Bayesian spatial prediction and sampling design. Spatial Statistics 1: 65-81, 2012

[4] G. Spoeck and J. Pilz: Spatial sampling design based on spectral approximations of the error process. In: Spatio-temporal design: Advances in Efficient Data Acquisition (W.G. Mueller and J. Mateu, Eds.), Wiley, New York 2013, 72-102

[5] G. Spoeck and J. Pilz: Simplifying objective functions and avoiding stochastic search algorithms in spatial sampling design. Front. Environ. Sci. 3:39: 1-22, 2015.

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Selfadjoint elliptic operators with boundary conditions on not closed hypersurfaces

**Speaker:**Prof. Dr. Andrea Mantile (Université de Reims Champagne-Ardenne)

**Date:**2.12.2015, 11:00 Uhr

**Room:**C307

**Abstract:**

The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on $\mathbb R^n$ with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Krein-like resolvent formulae where the reference operator coincides with the free operator with domain $H^2(\mathbb R^n)$; this provides an useful tool for the scattering problem from a hypersurface. Moreover, Schatten-von Neumann estimates, for the difference of the powers of resolvents of the free and the

perturbed operators, yield the existence and completeness of the wave operators of the associated scattering systems. This is a joint work with A. Posilicano and M. Sini

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Homological connectivity of random simplicial 2-complexes

**Speaker:**Oliver Cooley (TU Graz)

**Date:**Dienstag 17.11.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

Linial and Meshulam introduced a model of random simplicial 2-complexes with n 0-simplices (or vertices) in which all pairs of vertices form 1-simplices (or edges) and each triple of vertices forms a 2-simplex (or face) with probability p independently. They showed that this model undergoes a phase transition with respect to $\mathbb{F}_2$-homological 1-connectivity at around $p= \frac{2\log n}{n}$, and that the critical obstruction to connectivity is the presence of an edge which is in no face.

We consider a similar model, but in which each pair of vertices forms an edge only if it lies in a face. Thus the complex is generated by a random $3$-uniform hypergraph by taking the down-closure. Now by definition the previous critical obstruction to connectivity no longer exists. We show that in this model, the phase transition for $\mathbb{F}_2$-homological 1-connectivity occurs at around $p= \frac{\log n + \frac12 \log \log n}{n}$ and describe what the new critical obstruction is. The arguments are complicated by the fact that in this setting, connectivity is not a monotone property.

This talk is based on joint work with Penny Haxell, Mihyun Kang and Philipp Sprüssel.

#### Vortrag

**Title:**On surprising relations between Americans and Europeans

**Speaker:**Prof. Josef Teichmann (ETH Zürich)

**Date:**Freitag, 13.11.2015, 14:00

**Room:**Seminarraum für Statistik (NT03098)

**Abstract:**

Following work of Jourdain-Martini we shed some light on a surprising relationship between American and European options motivated by questions from Finance, Analysis and Numerics.

#### Zahlentheoretisches Kolloquium

**Title:**Parametric geometry of numbers

**Speaker:**Dr. Antoine Marnat (Université de Strasbourg)

**Date:**Freitag, 13. November 2015, 9:30 Uhr

**Room:**Seminarraum 2, Institut f. Geometrie, Kopernikusgasse 24, 4. Stock, TU Graz

**Abstract:**

#### Strukturtheorie-Seminar

**Title:**Fast factorization of hypergraph products

**Speaker:**Dr. Florian Lehner (Univ. Hamburg)

**Date:**Thursday, 12.11.2015, 11:00 c.t.

**Room:**Seminar room C307, Steyrergasse 30, 3rd floor

**Abstract:**

The existence of a unique decomposition into prime factors with

respect to the Cartesian product of both graphs and hypergraphs is

known since the 1960s. First polynomial time algorithms for the prime

factor decomposition of graphs were presented in the 1980s and even a

linear time algorithm (due to Imrich and Peterin) is known.

For hypergraphs the situation is different. Until recently no

polynomial time algorithm for the prime factorization was known, the

only such algorithm so far was presented by Bretto, Silvestre, and

Vallée in 2013. Its time complexity is $O(|E| |V| r^6 \Delta ^6)$

time, where $r$ is the rank of the hypergraph and $\Delta$ is the

maximal degree.

In this talk we outline a conceptually simpler an faster algorithm

which runs in $O(|E| |V| r^2)$, and in $O(|E| \log^2 |V|)$ for

bounded rank hypergraphs.

#### Strukturtheorie-Seminar

**Title:**Asymptotic behaviour of transition probabilities for subordinated random walk

**Speaker:**Dr. Wojciech Cygan (Univ. Wroclaw / TU Graz)

**Date:**Thursday, 5.11.2015, 11:00 c.t.

**Room:**Seminar room C307, Steyrergasse 30, 3rd floor

**Abstract:**

We construct a random walk $S_n^\psi$ in $\mathbb{Z}^d$, obtained by subordinating a strongly aperiodic random walk with finite range according to the concept of discrete subordination. The function $\psi$, which is the Laplace exponent of the subordinator is assumed to be a Bernstein function such that its behaviour at zero is prescribed in the realm of regularly varying functions. We prove a strong version of Tauberian type theorem which allows us to investigate the asymptotic behaviour of the tails of the subordinator. Finally, we find an asymptotic formula for the transition kernel of the subordinated random walk.

#### Festkolloquium aus Anlass des 60. Geburtstages von Prof. Dr. Maximilian Ganster

**Title:**Kolloquium aus Topologie

**Speaker:**Prof. Dr. Michael Kerber (TU Graz) Prof. Dr. Martin Goldstern (TU Wien) Prof. Dr. Jörg Thuswaldner (MU Leoben) ()

**Date:**Freitag, 30. Oktober 2015, ab 10 Uhr

**Room:**Vormittag: SR Geometrie 2, Kopernikusgasse 24, 4. Stock (im Rahmen der Advanced Topics in Discrete Mathematics) [2mm]Nachmittag: SR C208, Institut für Mathematik, Steyrergasse 30, 2.Stock

**Abstract:**

[5mm]

10:00: Kaffee[3mm]

10:30: Begrüßung[3mm]

10:45: Michael Kerber: Topological data analysis[3mm]

12:00: Mittagessen[3mm]

14:00: Martin Goldstern: p-points and ultrafilters without p-point quotients[3mm]

14:45: Musikalische Darbietung von Prof. Dr.Otto Laback[3mm]

15:15: Kaffeepause[3mm]

15:30: Jörg Thuswaldner: Topology of 3-dimensional fractals

#### Opening of the Second Phase

**Title:**... with talks by Prof. Ilse Fischer and Prof. Emo Welzl

**Speaker:**()

**Date:**Dienstag, der 27.10.2015, von 11:00 bis 15:30

**Room:**HS BE01, Steyrergasse 30, Erdgeschoss

**Abstract:**

Talks will be given by Prof. Ilse Fischer (University of Vienna) and Prof. Emo Welzl (ETH Zurich). Moreover, there will be two talks by students from the first phase; Mario Weitzer (Project 06) and Christopher Frei (Project 09). Please find further details on our website: www.math.tugraz.at/discrete

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Scaling limits and Benjamini-Schramm limits of some models of random trees, graphs and planar maps

**Speaker:**Benedikt Stufler (Ludwig-Maximalians-Universität München)

**Date:**Dienstag 20.10.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

We provide an overview of the speakers' scientific work, including the following topics. We establish the Brownian continuum random tree as the scaling limit of random unlabelled unrooted trees, and random graphs from subcritical classes, both in the labelled setting (joint work with K. Panagiotou and K. Weller) and in the unlabelled setting. We provide a new proof for the scaling limit of random P\'olya trees (joint with K. Panagiotou), extending previous results by treating trees with arbitrary vertex-degree restrictions in a unified way. We provide a new proof for the scaling limit of random outerplanar maps, extending previous results by treating maps with independent link weights and obtaining the scaling limit of random bipartite outerplanar maps. We establish Benjamini-Schramm limits of random graphs from subcritical graph classes (in the labelled and unlabelled settings) and classes of outerplanar maps satisfying a subcriticality condition. We use an elegant probabilistic approach in order to obtain scaling limits for the sizes of the $k$-th largest block in random labelled planar graphs, which seems to be a new result for $k \ge 2$.

#### Strukturtheorie-Seminar

**Title:**Boundary preserving transformations of random walks

**Speaker:**Prof. Vadim A. Kaimanovich (Univ. Ottawa)

**Date:**Thursday,15.10.2015, 11:00 c.t.

**Room:**Seminar room C307, Steyrergasse 30, 3rd floor

**Abstract:**

Given two different random walks on the same group, a priory there is no reason to expect them to have the same Poisson boundary. We shall show that there is a natural class of transformations of random walks (determined by ordinary or, more generally, randomized stopping times) which do not change the Poisson boundary. The related questions and conjectures will also be discussed.

#### Rigorosum - GEÄNDERTER HÖRSAAL

**Title:**Combinatorial and Probabilistic Aspects of Discrete Groups

**Speaker:**Johannes Cuno (TU Graz)

**Date:**Mittwoch, 14. Oktober 2015, 11 Uhr c.t.

**Room:**HÖRSAAL BE01, Steyrergasse 30, Erdgeschoß

**Abstract:**

My thesis consists of three projects, each of which focuses on a different aspect of infinite graphs and groups. This talk is part of my defence and I will give an overview over the methods used and the results obtained in my thesis.

ATTENTION: THE THESIS DEFENSE WILL TAKE PLACE IN LECTURE ROOM BE01, Steyrergasse 30, ground floor

#### Strukturtheorie-Seminar

**Title:**Taming the hydra: the Word Problem, Dehn functions, and extreme integer compression

**Speaker:**Prof. Tim Riley (Cornell University, USA)

**Date:**Mittwoch, 14. Oktober 2015, 15 Uhr c.t.

**Room:**Seminarraum A306, 3. Stock, Steyrergasse 30

**Abstract:**

For a finitely presented group, the Word Problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is the time-complexity of a direct attack on the Word Problem by applying the defining relations.

A ``hydra phenomenon'' gives rise to novel groups with extremely fast growing (Acker\-mannian) Dehn functions. I will explain why, nevertheless, there are efficient (polynomial time) solutions to the Word Problems of these groups. The main innovation is a means of computing efficiently with compressed forms of enormous integers.

This is joint work with Will Dison and Eduard Einstein.

#### Advanced Topics in Discrete Mathematics

**Title:**An invitation to groups and graphs arising from automata

**Speaker:**Dr. Daniele d'Angeli (TU Graz)

**Date:**Friday, 9.10.2015, 10:30

**Room:**SR II Geometrie, Kopernikusg. 24/IV

**Abstract:**

(Coffee break at 10:00 at the Geometry Institute)

#### Strukturtheorie-Seminar

**Title:**Algorithmic problems in automaton groups

**Speaker:**Prof. Ievgen Bondarenko (Taras Shevchenko National University of Kyiv, Ukraine)

**Date:**Freitag, 9. Oktober 2015, 11:30 Uhr

**Room:**Seminarraum 2 (Geometrie), Kopernikusgasse 24

**Abstract:**

This talk wants to present some recent results and open questions related to algorithmic problems in automaton groups. Note that it is preceded by an introductory talk given by Daniele D'Angeli at 10:30 in the same seminar room. The latter is part of the series Advanced Topics in Discrete Mathematics.

#### Gastvortrag

**Title:**Partially Observable Risk-Sensitive Markov Decision Processes

**Speaker:**Prof. Dr. Nicole Bäuerle (Karlsruher Institut für Technologie (KIT))

**Date:**Freitag, 9. Oktober 2015, 14:00 Uhr s.t.

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

We consider the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite time horizon which is generated by a Partially Observable Markov Decision Process (POMDP). In contrast to a risk-neutral decision maker this optimization criterion takes the variability of the cost into account. It contains as a special case the classical risk-sensitive optimization criterion with an exponential utility. We show that this optimization problem can be solved by embedding the problem into a completely observable MDP with extended state space and give conditions under which an optimal policy exists. The state space has to be extended by the joint conditional distribution of current unobserved state and accumulated cost. In case of an exponential utility, the problem simplifies considerably and we rediscover what in previous literature has been named information vector. However, since we do not use any change of measure techniques here, our approach is simpler. A small numerical example, namely the classical repeated casino game with unknown success probability is considered to illustrate the influence of the certainty equivalent and its parameters. The talk is based on joint work with Ulrich Rieder.

#### Vortrag

**Title:**On the fibration method in analytic number theory

**Speaker:**Dr. Efthymios Sofos (Leiden)

**Date:**Donnerstag, 8. Oktober 2015, 11.00 Uhr s.t.

**Room:**Seminarraum A206, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

The fibration method, very broadly, refers to the situation where one

establishes a required property for a variety by fibering it into

simpler varieties known to satisfy the said property. Its use in

arithmetic geometry has been made chiefly in the context of the

Brauer-Manin obstruction, for example in the works of Swinnerton-Dyer

and Colliot-Thélène and most recently in that of Harpaz and Wittenberg.

In this talk we will show that this method can be developed within the

context of analytic number theory with the aim of tackling a range of

important problems. Our first result regards obtaining correct lower

bounds for Manin's conjecture for smooth del Pezzo surfaces of degree

$>1$ which have a conic bundle structure. One should notice that the

conjecture has not been established for these varieties and there were

previously only weak upper bounds in degree 3 and a scarcity of

results in degree 2. The second problem we shall refer to is known as

the Sarnak saturation number: Given a variety V defined over the

rationals, it is defined as the least integer r(V) such that rational

points with at most r prime factors are Zariski dense in V. We shall

show that varieties fibered into unirational varieties have finite

saturation. This covers many new low dimensional cases unassailable by

other analytic methods hitherto used in this problem.

#### Strukturtheorie-Seminar

**Title:**On a free local limit theorem and its applications

**Speaker:**Gennadii Chistyakov (Universität Bielefeld)

**Date:**1.10.2015, 11:00 c.t.

**Room:**SR C307, Steyrergasse 30, 3.Stock

**Abstract:**

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Random planar graphs with n vertices and m edges

**Speaker:**Chris Dowden (London School of Economics)

**Date:**Dienstag 29.9.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

Let $P_{n,m}$ denote a graph taken uniformly at random from the set of all labelled planar graphs with $n$ vertices and $m(n)$ edges. We shall use counting arguments to explore the probability that $P_{n,m}$ has a component or subgraph isomorphic to $H$, for various fixed $H$, as $n \to \infty$. In particular, we will investigate exactly when the probabilities are bounded away from $0$ and/or $1$, showing that there is different behaviour depending on both the graph $H$ and the ratio $m/n$.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Random graphs: sandwiching, subgraph counts extension statements

**Speaker:**Matas Šileikis (University of Oxford)

**Date:**Freitag 25.9.2015, 14:15

**Room:**Seminarraum C307, Steyrergasse 30, 3. Stock

**Abstract:**

In this talk I will present some results on random graphs. First result (joint with A. Dudek, A. Frieze and A. Rucinski) concerns embedding of the random graph $G(n,m)$ into the random $d$-regular graph $R(n,d)$, where $m \sim nd/2$. This allows to transfer monotone increasing properties from $G(n,m)$ to $R(n,d)$. In the remaining time I will cover some results on the subgraph counts in the random graph $G(n,p)$ (the ``infamous upper tail'' problem) as well as joint work with L. Warnke on extension statements (a generalization of the fact that whenever $np

\gg \log n$, the degree sequence of $G(n,p)$ is concentrated around $np$).

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Completeness of resonant states for Helmholtz resonator and factorization of the characteristic function

**Speaker:**Prof. Dr. Igor Popov (ITMO University, St. Petersburg)

**Date:**30.9.2015, 14:15 Uhr

**Room:**C307

**Abstract:**

The Dirichlet (or Neumann) Laplacian in a bounded domain has a complete set of eigenfunctions. If there is an opening in the boundary (the Helmholtz resonator) then eigenvalues turn into resonances (quasi-eigenvalues) and eigenfunctions to resonant states (quasi-eigenfunctions). The completeness of the set of resonant states is considered in the framework of the zero-width slit model. The relation with the problem of factorization of the characteristic function in the

Sz.-Nagy--Foias functional model is discussed.

#### Strukturtheorie-Seminar

**Title:**Unimodality of Free Levy Processes

**Speaker:**Takahiro Hasebe (Hokkaido University)

**Date:**17.9.2015, 15:00 c.t.

**Room:**SR C307, Steyrergasse 30, 3.Stock

**Abstract:**

A probability distribution is called unimodal} if it is the weak limit of probability measures whose densities have unique peaks, for example the Gaussian, the semicircle law and the uniform distribution. In this talk I will show that any selfdecomposable free Levy process has unimodal marginal distributions. Also, I will show that any bounded free Levy process has unimodal marginal distributions in large time. These results are based on joint work with Steen Thorbjornsen and Noriyoshi Sakuma.

#### Strukturtheorie-Seminar

**Title:**Poincaré und Multityp-Galton-Watson-Prozesse

**Speaker:**PD. Dr. Elmar Teufl (Univ. Tübingen)

**Date:**Wednesday, 26.8.2015, 11:00 c.t.

**Room:**Seminar room C307, Steyrergasse 30, 3rd floor

**Abstract:**

Henri Poincaré hat in einer Arbeit aus dem Jahr 1890 endliche Familien von Funktionen, welche einem Multiplikationsgesetz genügen, studiert. Falls die Familie nur aus einer Funktion $f$ besteht, dann erfüllt diese die sogenannte Poincaré-Gleichung $f(mx) = R(f(x))$, wobei $R$ und $m$ gegeben sind. Lösungen $f$ dieser Funktionalgleichung werden in der Iterationstheorie und in der Theorie von Galton-Watson-Prozesse verwendet. Letzteres geht auf die Dissertation von Theodore E. Harris aus dem Jahr 1947 zurück. In beiden Fällen scheint die Arbeit von Poincaré in neuerer Literatur nur im Kontext des eindimensionalen Fall zitiert zu werden. Während in der Iterationstheorie der mehrdimensionale Fall von eingeschränkten Interesse ist, entspricht der mehrdimensionale Fall genau den Anforderungen bei Multityp-Galton-Watson-Prozessen. Im Vortrag werden diese Anwendungen zusammen mit Folgerungen aus Harris’ Dissertation diskutiert.

#### Vortrag im Seminar Optimierung und Diskrete Mathematik

**Title:**On the k-opt neighborhood for TSP

**Speaker:**Gerhard J. Woeginger (Department of Mathematics and Computer Science, TU Eindhoven)

**Date:**Neuer Termin {\bf 10.8. 2015}, 15:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

One of the most popular local search heuristics for the Travelling

Salesman Problem (TSP) is centered around the k-opt neighborhood;

k-opt tries to improve a (suboptimal) tour by removing k edges and

by reconnecting the resulting pieces into a new tour through the

insertion of k new edges.

In the talk, I will concentrate on the problem whether a given tour

is a local optimum for k-opt (for some fixed k), and I will present

a fine-grained complexity analysis of this problem.

#### Strukturtheorie-Seminar

**Title:**B-Valued Free Convolution for Unbounded Operators

**Speaker:**John Williams (Universität des Saarlandes)

**Date:**21.7.2015, 11:15

**Room:**SR C307, Steyrergasse 30, III. Stock

**Abstract:**

Consider the $\mathcal{B}$-valued probability space $(\mathcal{A}, E, \mathcal{B})$, where $\mathcal{A}$ is a tracial von Neumann algebra. We extend the theory of operator valued free probability to the algebra of affiliated operators $\tilde{\mathcal{A}}$. For a random variable $X \in \tilde{\mathcal{A}}^{sa}$ we study the Cauchy transform $G_{X}$ and show that the operator algebra $(\mathcal{B} \cup \{X\})''$ can be recovered from this function. In the case where $\mathcal{B}$ is finite dimensional, we show that, when $X, Y \in \tilde{\mathcal{A}}^{sa}$ are assumed to be $\mathcal{B}$-free, the $\mathcal{R}$-transforms are defined on universal subsets of the resolvent and satisfy $$ \mathcal{R}_{X} + \mathcal{R}_{Y} = \mathcal{R}_{X + Y}. $$ Examples indicating a failure of the theory for infinite dimensional $\mathcal{B}$ are provided. Lastly, we show that the class of functions that arise as the Cauchy transform of affiliated operators is, in a natural way, the closure of the set of Cauchy transforms of bounded operators.

#### Vortrag im Rahmen des Symposium on Geometry Processing

**Title:**Solving the 3-D Puzzle of Rotation Assignment in Single Particle Cryo-Electron Microscopy

**Speaker:**Amit Singer (Princeton University)

**Date:**7.7.2015, 9:15-10:15

**Room:**Hörsaal H, Kopernikusgasse 24, EG (Chemietrakt)

**Abstract:**

Single particle cryo-electron microscopy (EM) recently joined X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy as a high-resolution structural method for biological macromolecules. In single particle cryo-EM, the 3-D structure needs to be determined from many noisy 2-D projection images of individual, ideally identical frozen-hydrated macromolecules whose orientations and positions are random and unknown (i.e., random X-ray transform). This lecture will explore algorithms for estimating the unknown pose parameters. The main focus will be on semidefinite programming relaxations that are based on the Fourier transform over the group SO(3). Such semidefinite programs can be viewed as extensions to existing approximation algorithms to max-cut and unique games, two fundamental problems in theoretical computer science. The approach is quite general and can be used to handle other groups of transformations that arise in other applications in signal processing, image analysis, computer vision and computer graphics

#### Zahlentheoretisches Kolloquium - Vortrag abgesagt

**Title:**Vortrag abgesagt

**Speaker:**Univ.-Prof. Dr. Ulrich Dieter (TU Graz)

**Date:**Freitag, 3. 7. 2015, 14:00 Uhr, c.t.

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

Leider muss der Vortrag von Prof. Dr. Ulrich Dieter am 3. 7. 2015 aus gesundheitlichen Gründen abgesagt werden.

#### Mathematisches Kolloquium

**Title:**Arithmetic Harmonic Analysis

**Speaker:**Prof. Dr. Jörg Brüdern (Georg-August-Universität Göttingen)

**Date:**Freitag, 3. 7. 2015, 11:00 Uhr Kaffee: 10:30 Uhr

**Room:**Vortrag: SR Statistik, Kopernikusg. 24, 3.Stock Kaffee: Inst. f. Geometrie, Kopernikusg. 24, 4.Stock

**Abstract:**

Abstract:

We discuss recent work with Trevor Wooley concerning

the diophantine analysis of cubic and quartic forms.

In a series of papers, the Hasse principle for systems

of such forms has been established by novel harmonic analysis

where Weyl sums of partial arithmetic nature play

a peculiar role. The talk will survey these developments.

#### Strukturtheorie-Seminar

**Title:**Interplay between group and graph structure in the theory of topological groups

**Speaker:**Prof. Rögnvaldur I. Möller (University of Iceland)

**Date:**Thursday, 2.7.2015, 11:00 c.t.

**Room:**Seminar room C307, Steyrergasse 30, 3rd floor

**Abstract:**

An Abels-Cayley graph for a compactly generated totally disconnected locally compact group is a locally finite connected graph that the group acts transitively on such that stabilizers of vertices are compact open subgroups. In this talk I will survey some old and new results about how the structure of the group is reflected in the graph and vice versa.

#### Strukturtheorie-Seminar

**Title:**Matrix coefficient realization theory of noncommutative rational functions

**Speaker:**Jurij Volčič (University of Auckland)

**Date:**Mittwoch 1.Juli 2015, 11:15 Uhr

**Room:**SR C307, Steyrergasse 30, III. Stock

**Abstract:**

One of the main reasons why noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, are so inaccessible, is their lack of a canonical form. For rational functions defined at 0 this can be compensated by using realizations, which originated in automata theory and systems theory. The aim of this talk is to present a realization theory that is applicable to every noncommutative rational function and is adapted for studying its finite-dimensional evaluations. Using these matrix coefficient realizations we can measure the complexity of noncommutative rational functions, describe their singularities and assert size bounds for the rational identity testing problem. The self-adjoint version will be also considered.

#### Mathematisches Kolloquium im Rahmen des Doktoratskollegs

**Title:**Cellular Automata

**Speaker:**B\'ela Bollob\'as (University of Cambridge und University of Memphis)

**Date:**Dienstag 30.6.2015, 10:30 (Anschließend Mittagsbuffet)

**Room:**Hörsaal BE01, Steyrergasse 30, Erdgeschoss

**Abstract:**

A cellular automaton, introduced in the 1940s by von Neumann after a suggestion of Ulam, is an interacting particle system: a collection of sites of a grid or a grid-like graph, with each site in one of finitely many ‘states’. Starting with a certain configuration (distribution of sites), at each time-step the system updates itself according to some fixed rules: each site goes into a state that depends only on the states of a few nearby sites. Examples include the Ising model of ferromagnetism, many simple models of the brain, and Conway’s ‘Game of Life’. Despite much effort over the last fifty years, a general theory of cellular automata still seems very far out of reach.

In my talk I shall give a brief introduction to some aspects of cellular automata, concentrating on bootstrap percolation. Although I shall consider extremal problems concerning bootstrap percolation, the emphasis will be on processes in random environments. I shall end with a number of very recent results on cellular automata with the most general local, homogeneous and monotone update rules. These general processes were introduced by Smith, Uzzell and me, and the results I shall present have been proved by Smith, Uzzell, Balister, Przykucki, Duminil-Copin, Morris, and me.

\vspace{2cm}

This event is generously supported by the ÖMG.

#### Mathematisches Kolloquium

**Title:**On factorizations of analytic operator-valued functions and eigenvalue multiplicity questions

**Speaker:**Prof. Dr. Fritz Gesztesy (University of Missouri, Columbia)

**Date:**26.6.2015, 13:30 Kaffee im Foyer, 14:00 Vortrag

**Room:**Hörsaal BE01, Steyrergasse 30

**Abstract:**

We study several natural multiplicity questions that arise in the context of the

Birman-Schwinger principle when applied to non-self-adjoint operators. In particular, we study factorizations of analytic operator-valued functions and re-derive some of Howland's results in this connection and subsequently extend them.

Considering algebraic multiplicities of finitely meromorphic operator-valued functions, we recall the notion of the index of a finitely meromorphic operator-valued function and use that to prove an analog of the well-known Weinstein-Aronszajn formula relating algebraic multiplicities of the underlying unperturbed and perturbed operators. If time permits, we may discuss an additional application to the index of a pair of orthogonal projections.

This is based on joint work with H. Holden (Trondheim) and R. Nichols (Chattanooga).

**Title:**Doctoral School Seminar

**Speaker:**()

**Date:**26.6.2015, 10:30-13:00

**Room:**Seminarraum 2, Institut f. Geometrie

**Abstract:**

#### Vortrag

**Title:**Establishing a Common Agricultural Policy Monitoring and Evaluation Framework & Support of an Advisory Service System

**Speaker:**Aleksandra Figurek (Facutly of Agriculture, University of Banja Luka, Republic of Srpska, Bosnia & Herzegovina)

**Date:**26. Juni 2015, 11:00 Uhr

**Room:**SR für Statistik (NT03098), Kopernikusgasse 24/III

**Abstract:**

Nowadays, a common problem is the existence of different data sources, in the sense of lack of prototyping. The objective of this work is to present a solution for the lack of communication between the different data sources and the lack of prototyping.

The solution proposed is based on the ontology-driven knowledge management and meta-data engineering and includes an example from the real world.

#### Vortrag im Seminar Optimierung und Diskrete Mathematik

**Title:**Group activity selection from ordinal preferences

**Speaker:**Andreas Darmann (Institut für Finanzwissenschaft, Universität Graz)

**Date:**23.6. 2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

We consider the situation in which group activities need to be organized

for a set of agents when each agent can take part in at most one activity. The

agents' preferences depend both on the activity and the number of participants

in that activity. In particular, the preferences are given by means of strict orders over such pairs (activity, group size), including the possibility ``do nothing''. Our goal will be to assign agents to activities on basis of their preferences, the minimum requirement being that no agent prefers doing nothing, i.e., not taking part in any activity at all. We take three different approaches to establish such an assignment:

(i) by use of k-approval and Borda scores; (ii) considering stability

concepts such as Nash and core stability; (iii) applying the Condorcet criterion.

For each of these approaches, we analyse the computational complexity

involved in finding a desired assignment. Particular focus is laid on two natural special cases of agents' preferences which allow for positive complexity results.

#### SFB-Kolloquium

**Title:**Geometry optimization in carbon

**Speaker:**Prof. Dr. Ulisse Stefanelli (Univ. Wien)

**Date:**Freitag, 19. 6. 2015, 14:00 c.t.

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

Carbon nanostructures such as graphene, nanotubes, and fullerenes are

locally planar: each atom forms three covalents bonds which (ideally)

create bonding-angles of $2\pi/3$. In distinguished regimes, this

phenomenology can be modeled by minimizing specific atomic-interaction

potentials including

three-body interaction terms [T].

I intend to review some of the existing crystllization results for this

kind of potentials [E,M,M2]. In particular, I will focus on the

possibility of characterizing the geometry of energy minimizers,

especially in three-dimensions. The stability, fine geometry, and partly

the nanomechanics of classes

of nanotubes and fullerenes will be discussed. This is joint work with

M. Friedrich, E. Mainini,

H. Murakawa, and P. Piovano.

[E] W. E, D. Li. On the crystallization of 2D hexagonal lattices. Comm.

Math. Phys. 286 (2009) 1099-1140.

[M] E. Mainini, U. Stefanelli. Crystallization in carbon nanostructures.

Comm. Math. Phys. 328 (2014) 545-571.

[M2] E. Mainini, P.Piovano, U. Stefanelli. Finite crystallization in the

square lattice. Nonlinearity, 27 (2014) 717-737.

[T] J. Tersoff. New empirical approach for the structure and energy of

covalent systems. Phys. Rev. B 37 (1988) 6991-7000.

#### Advanced Topics in Discrete Mathematics

**Title:**Old and new results about the register function

**Speaker:**Helmut Prodinger (Stellenbosch University)

**Date:**19.6.2015, 10:30

**Room:**Seminarraum 2 Geometrie, 4. Stock, Kopernikusgasse 24

**Abstract:**

The register function of binary trees is also known as the Horton-Strahler numbers and is a very natural concept. Recently I detected a new approach, based on substitutions. With it, results of two Japanese physicists could be improved. I will also talk about some older material, in particular about a problem of Yekutieli and Mandelbrot that I was able to solve several years ago.

#### Strukturtheorie-Seminar

**Title:**Boundaries of hyperbolic groups and combination problems

**Speaker:**Dr. Alexandre Martin (Universität Wien)

**Date:**Thursday, 18.6.2015, 11:00 c.t.

**Room:**Seminar room C307, Steyrergasse 30, 3rd floor

**Abstract:**

Given a group acting on a tree, a natural problem is to understand properties of the group by understanding properties of the stabilisers of vertices and the geometry of the action. As an example, I will explain how the Gromov boundary of a hyperbolic group splitting as free product A*B depends only on the Gromov boundaries of the hyperbolic groups A and B (joint work with J. Swiatkowski). More generally, given a group acting cocompactly on a hyperbolic complex, I will explain conditions under which it is possible to recover the hyperbolicity of the group directly from the action and to understand the Gromov boundary of the group by means of the various Gromov boundaries at hand. (part of this is joint work with D. Osajda)

#### Strukturtheorie-Seminar

**Title:**Biased random walks among random conductances

**Speaker:**Prof. Dr. Nina Gantert (TU München)

**Date:**Thursday 11.6.2015, 11 Uhr c.t.

**Room:**SR C307, Steyrergasse 30, 3rd floor

**Abstract:**

We consider a random walk among iid, bounded conductances and prove the Einstein relation which relates its diffusivity to the derivative at zero of the velocity of a biased random walk among the same random conductances.

We show that the velocity is differentiable as a function of the bias, and that it is in general not increasing.

The talk is based on joint works in progress with Noam Berger, Jan Nagel and Xiaoqin Guo.

#### Vortrag im Rahmen des Seminars TM (Angewandte Analysis und Numerische Mathematik)

**Title:**Adaptive Coupling of Finite Volume and Boundary Element Methods

**Speaker:**Jun.-Prof. Dr. Christoph ERATH (TU Darmstadt)

**Date:**Dienstag, 9.6.2015, 14:15 Uhr

**Room:**TU Graz, Steyrergasse 30, 3. Stock, Seminarraum C307

**Abstract:**

#### Strukturtheorie-Seminar

**Title:**Intersection graphs of groups

**Speaker:**Selcuk Kayacan (Istanbul Technical University)

**Date:**Monday, 8 June 2015, 11:00 c.t.

**Room:**Seminar room A306, Steyrergasse 30, 3rd floor

**Abstract:**

For a group G the intersection graph of G is a simple graph such that its vertex set consists of the non-trivial proper subgroups of G and two distinct vertices are joined by an edge if and only if their intersection is non-trivial. We have classified all finite groups whose intersection graphs are planar and showed that finite abelian groups can almost be characterized by their intersection graphs. In this talk, I will outline those results and present some speculations on possible further directions.

Mr. Kayacan is a PhD student from Istanbul holding a Turkish TÜBITAK grant at Institut für Math. Strukturtheorie for the next 12 months.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Enumeration of cubic multigraphs on orientable surfaces

**Speaker:**Michael Moßhammer (TU Graz)

**Date:**Dienstag 2.6.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

In recent years there have been various results in counting graphs embeddable on orientable surfaces, especially for planar graphs. For example the number of embeddable graphs with $n$ vertices and $m$ edges with $m<n$ is known for planar graphs but not for graphs embeddable on surfaces of higher genus.

One way to count such graphs is a constructive decomposition resulting in the problem of counting cubic multigraphs on orientable surfaces.

In this talk we will show the asymptotic number of cubic multigraphs embeddable on an orientable surface of genus $g$ to be asymptotically

\[c_g \gamma^nn^{5/2(g-1)-1}n!,\]

where $c_g$ is a constant depending on the genus and the growth constant $\gamma$ is independent of the genus. To do this, methods from analytic combinatorics and structural graph theory will be used as well as results from Gao on triangulations.

In a second part of the talk, we will show how the above result can be used to study the number and the structure of general graphs embeddable on a surface.

#### Zahlentheoretisches Kolloquium

**Title:**Strange products of projections

**Speaker:**Prof. Dr. Eva Kopecká (Universität Innsbruck)

**Date:**Freitag, 29. 5. 2015, 14:00 s.t.

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

Let X and Y be two closed subspaces of a Hilbert space.

If we send a point back and forth between them by orthogonal projection,

the iterates converge according to von Neumann to the projection of the point onto the intersection of X and Y.

If $H$ is an infinite dimensional Hilbert space, there exist three orthogonal projections $X_1, X_2, X_3$ onto closed subspaces of $H$, $z_0\in H$ and a sequence of indices $k_1, k_2,\dots \in \{1,2,3\}$ so that the sequence of iterates defined by $z_n= X_{k_n} z_{n-1}$ does not converge in norm.

We will explain how this implies that in every infinite dimensional Hilbert space there exist three orthogonal projections $X_1, X_2, X_3$ onto closed subspaces of $H$ such that for {\it every} $0\ne z_0\in H$ there exist $k_1, k_2,\dots \in \{1,2,3\}$ so that the sequence of iterates $\{z_n\}_{n=0}^{\infty}$ does not converge in norm.

#### Strukturtheorie-Seminar

**Title:**Excited Mob

**Speaker:**Tal Orenshtein (Université Lyon 1)

**Date:**Donnerstag, 28. Mai 2015, 11:00 Uhr

**Room:**RAUMÄNDERUNG!!! NEUER RAUM: Seminarraum 1, Institut für Geometrie (NT04060)

**Abstract:**

Consider two generalizations of Excited random walk:

A) $k$ Cookie walkers share a cookie environment and move according to some scheduling. (We call this ``$k$-mob walk''.)

B) There are $k$ Cookie walkers, each one in turn perform infinitely many steps on the $(j-1)$-time leftover environment, $j=1,\ldots,k$.

In the talk we shall present the following result, and discuss ideas from its proof. For the one dimensional model, assume the standard conditions on the cookie distribution: i.i.d., elliptic and bounded, then we have in both cases A) and B) that

(i) all the walkers are transient to the right a.s. if and only if $\delta>k$, and

(ii) they all have positive speed if and only if $\delta>k+1$, where $\delta$ is the expected total drift per site.

In particular, when $\delta>3$, the walker on the (1st) leftover environment is an example of a ballistic Cookie walk with cookie distribution which is not a trivial modification of an i.i.d. one (but has some ergodic properties, and moreover, when appropriately redefining ``leftover environment'', it can be made stationary and ergodic).

A fundamental ingredient of the proof is an ``Abelian'' property of the deterministic cookie model, where the walkers follow pregiven instructions, or ``arrows'', rather than cookies.

This is joint work with Gideon Amir.

#### Vortrag im Rahmen des Seminars TM (Angewandte Analysis und Numerische Mathematik)

**Title:**Discretization error estimates for Dirichlet boundary control problems

**Speaker:**Dr. Johannes PFEFFERER (Universität der Bundeswehr München)

**Date:**Mittwoch, 27.5.2015, 10:00 Uhr

**Room:**TU Graz, Steyrergasse 30, 3. Stock, Seminarraum C307

**Abstract:**

#### Strukturtheorie-Seminar

**Title:**On Random Subspaces of Matrices and Free Compression norms

**Speaker:**Ion Nechita (TU München)

**Date:**Donnerstag, 21.Mai 2015, 11:15 Uhr

**Room:**SR A206, Steyrergasse 30, II. Stock

**Abstract:**

We study not one, but a whole subspace of random rectangular matrices. In the limit of large dimension, we show that the set of eigenvalues of these matrices converges to a limit that can be described with the help of a norm arising in free probability theory. We show how to optimize $L_p$ norms and entropy over these sets of eigenvalues and we present some applications to quantum information theory. This is joint work with Serban Belinschi and Benoit Collins.

#### Strukturtheorie-Seminar

**Title:**Sample Variance in Free Probability

**Speaker:**Wiktor Ejsmont (Universität Wroclaw)

**Date:**Donnerstag, 21.Mai 2015, 10:15 Uhr

**Room:**SR A206, Steyrergasse 30, II. Stock

**Abstract:**

#### Strukturtheorie-Seminar

**Title:**On the spectrum in max-algebra

**Speaker:**Aljoša Peperko (Univerza v Ljubljani)

**Date:**Dienstag, 12. Mai 2015, 10:15 Uhr

**Room:**Seminarraum 2, Institut für Geometrie

**Abstract:**

The algebraic system max algebra and its isomorphic versions (max-plus algebra, tropical algebra) provide an attractive way of describing a class of non-linear problems appearing for instance in manufacturing and transportation scheduling, information technology, discrete event-dynamic systems, combinatorial optimization, mathematical physics, DNA analysis, ...

Max algebra's usefulness arises from a fact that these non-linear problems become linear when described in the max algebra language. Moreover, recently max algebra techniques were used to solve certain linear algebra problems. For $n\times n$ non-negative matrices, the role of the spectral radius in max-algebra is played by the maximum cycle geometric mean. For more general max type operators this role is taken over by the Bonsall's cone spectral radius.

The talk will consist of three parts. In the first part the description of the eigenvalues in max-algebra will be presented via local radii of standard vectors.

In the second part of the talk, we will present the main ideas of a short and elemenatary max-algebra based proof of the well known Berger-Wang formula in the case of bounded subsets of $n\times n$ non-negative matrices. The Berger-Wang formula is an equality between the generalized and the joint spectral radius of a given bounded set of matrices. In the third part of the talk, some recent results for more general max-type operators will be presented. In particular that the Bonsall's cone spectral radius of such operators is included in the approximative point spectrum.

This results are part of the joint work with Vladimir Müller. Some open questions will also be included in the talk.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**A special case of the data arrangement problem on binary trees

**Speaker:**Rostislav Stan\v{e}k (TU Graz)

**Date:**Dienstag 12.5.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

The data arrangement problem on regular trees (DAPT) consists of assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges of G is minimised. Luczak and Noble have shown that this problem is NP-hard for every fixed $d \ge 2$. The question about the computational complexity of the DAPT in the case where the guest graph is a tree is still open.

We deal with one special case of this problem where both the guest and the host graph are binary regular trees. First, we provide a solution algorithm which clearly yields an upper bound. Then we introduce and solve the k-balanced partitioning problem (k-BPP}) of a binary regular tree for particular choices of k and show that a lower bound for the original problem can be derived by solving $h$ instances of k-BPP, where $h$ is the height of the host graph T.

By combining both bounds we obtain an approximation algorithm for our special case of DAPT.

Joint work with Eranda {\c C}ela and Joachim Schauer

#### Kolloquium Finanz- und Versicherungsmathematik

**Title:**

**Speaker:**()

**Date:**Freitag, 8.5.2015, 11:30 - 12:20, 14:00 - 16:10

**Room:**Vormittag: SR Geometrie, Kopernikusg.24, 4.St.Nachmittag: SR C208, Steyrerg.30, 2.St.

**Abstract:**

Programm:[2mm]

11:30 Eröffnung durch Univ.Prof. Dr. Robert Tichy[5mm]

11:35 Univ.Prof. Dr. Thorsten Rheinländer (TU Wien)

Financial markets with a large trader[5mm]

12:20 Mittagspause[5mm]

14:00 Assoz.Univ.Prof. Dr. Gunther Leobacher (JKU Linz)

A numerical method for SDEs with discontinuous drift[5mm]

14:45 MScAS. Arian Cani (Université de Lausanne)

Maximizing the expected discounted surplus[5mm]

15:15 Pause[5mm]

15:30 Dr. Markus Hofer (ING Amsterdam)

Wrong way risk in credit valuation adjustments[5mm]

16:10 Ende[5mm]

Abstracts: https://www.math.tugraz.at/~thonhau/abstracts_2015.pdf

#### Zahlentheoretisches Kolloquium

**Title:**Diophantine equations with Bernoulli polynomials

**Speaker:**Dr. Gökhan Soydan (Uludag University, Bursa/Turkey)

**Date:**Donnerstag, 7. Mai 2015, 17:00 s.t.

**Room:**Seminarraum A306, 3.Stock, Geodäsie, Steyrergasse 30

**Abstract:**

What I mean: I will prove that the Diophantine equation $(x+1)^k+(x+2)^k+...+(lx)^k=y^n$ has only finitely many solutions.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Arithmetic Removal Lemmas and Independent Sets in Hypergraphs

**Speaker:**Juanjo Rué (Freie Universität Berlin)

**Date:**Dienstag 5.5.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

In the last years, several authors have studied sparse and random analogues of a wide variety of results in extremal combinatorics. Very recently, due to the work of Balogh, Morris, and Samotij, and the work of Saxton and Thomason on the structure of independent sets on hypergraphs, several of these questions have been addressed in a new framework by using the so-called containers in hypergraphs.

In this talk I will present how to use this technology together with arithmetic removal lemmas due to Serra, Vena and Kral in the context of arithmetic combinatorics. We will show how to get sparse (and random) analogues of well-known additive combinatorial results even in the non-abelian situation.

This talk is based on a work in progress joint with Oriol Serra and Lluís Vena.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Algorithms and automata for the Tower of Hanoi\footnote{\copyright A.M.Hinz 2015}

**Speaker:**Andreas Hinz (LMU Munich & University of Maribor)

**Date:**Dienstag 28.4.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

Mathematical solitaire games like the Chinese Rings and the Tower of Hanoi can be modelled by state graphs, leading to the two-parameter classes of Sierpi\'{n}ski graphs $S_p^n$ and Hanoi graphs $H_p^n$. Shortest path algorithms can be based on automata in the Sierpi\'{n}ski case, so that the metric properties of $S_p^n$ (and $H_3^n\cong S_3^n$) are now completely understood. For Hanoi graphs with $p>3$, however, the notorious Frame-Stewart Conjecture (1941) is still undecided and unexpected behavior of eccentricities like Korf's Phenomenon (2004) remains unexplained. Wheras diam$(S_p^n)=2^n-1$ for all $p\geq 2$, the diameter of $H_p^n$ is known only for small values of the parameters by computer experiments.

\noindent {\bf References.}

\noindent [1] Hinz, A.M., Klav\v{z}ar, S., Milutinovi\'{c}, U., Petr, C., The Tower of Hanoi---Myths and Maths, Springer, Basel, 2013.

\noindent [2] Hinz, A.M., Holz auf der Heide, C., An efficient algorithm to determine all shortest paths in Sierpi\'{n}ski graphs, Discrete Appl.~Math.~177(2014), 111--120.

**Title:**Doctoral School Seminar

**Speaker:**()

**Date:**24.4.2015, 10:30-13:00

**Room:**Seminarraum 2, Institut f. Geometrie

**Abstract:**

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Morphing planar graphs

**Speaker:**Penny Haxell (University of Waterloo)

**Date:**Dienstag 21.4.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

Consider two straightline planar drawings G and H of the same planar triangulation, in which the outer face is fixed. A morph between G and H is a continuous family of drawings of the triangulation, beginning with G and ending with H. We say a morph between G and H is planar if each intermediate drawing is a straightline planar drawing of the triangulation. A morph is called linear if each vertex moves from its initial position in G to its final position in H along a line segment at constant speed. It is not difficult to see that in general the linear morph from G to H will not be planar.

Here we consider the algorithmic problem of finding a planar morph between two given drawings G and H with fixed outer face. For various reasons it is desirable to find morphs in which each vertex trajectory is fairly simple. Thus we focus on the problem of constructing a planar morph consisting of a polynomial number of steps, in which each step is a planar linear morph.

(Joint work with Fidel Barrera-Cruz and Anna Lubiw.)

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Periodic differential operators with predefined spectral gaps

**Speaker:**Dr. Andrii Khrabustovskyi (Karlsruhe Institute of Technology)

**Date:**11.5.2015, 14:00 Uhr

**Room:**C307

**Abstract:**

It is well-known (see, e.g., [1]) that the spectrum of self-adjoint periodic differential operators has a band structure, i.e. it is a locally finite union of compact intervals called bands}. In general the bands may overlap. The bounded open interval $(a,b)\subset\mathbb{R}$ is called a gap} if it has an empty intersection with the spectrum, but its ends belong to it.

The presence of gaps in the spectrum is not guaranteed: for example, the spectrum of the Laplacian in $L_2(\mathbb{R}^n)$ has no gaps, namely $\sigma(-\Delta_{\mathbb{R}^n})=[0,\infty)$. Therefore the natural problem is a

construction of periodic operators with non-void spectral gaps. The importance of this problem is caused by various applications, for example in physics of photonic crystals. We refer to the overview [2], where a lot of examples are discussed in detail.

Another important question arising here is how to control the location of the gaps via a suitable choice of the coefficients of the operators or/and via a suitable choice of the geometry of the medium. In the talk we give an overview of the results obtained in [3,4,5,6], where this problem is studied for various classes of periodic differential operators.

In a nutshell, our goal is to construct an operator (from some given class of periodic operators) such that its spectral gaps are close (in some natural sense) to predefined intervals.

\begin{thebibliography}{99}

\bibitem{E} M. Eastham, The spectral theory of periodic differential equations,

Scottish Academic Press, 1973.

\bibitem{HP} R. Hempel, O. Post, Spectral Gaps for Periodic Elliptic Operators

with High Contrast: an Overview, Progress in Analysis, Proceedings

of the 3rd International ISAAC Congress Berlin 2001, Vol. 1,

577-587, 2003; arXiv:math-ph/0207020.

\bibitem{1}

A. Khrabustovskyi, Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace-Beltrami operator, {Journal of Differential Equations, 252(3) (2012), 2339--2369.}

\bibitem{2}

A. Khrabustovskyi, Periodic elliptic operators with asymptotically preassigned spectrum, {Asymptotic Analysis, 82(1-2) (2013), 1-37.}

\bibitem{3}

A. Khrabustovskyi,

Opening up and control of spectral gaps of the Laplacian in periodic domains,

{Journal of Mathematical Physics, 55(12) (2014), 121502.}

\bibitem{4}

D. Barseghyan, A. Khrabustovskyi,

{Gaps in the spectrum of a periodic quantum graph with periodically distributed $\delta'$-type interactions}, submitted, {arXiv:1502.04664}.

\end{thebibliography}

#### Strukturtheorie-Seminar

**Title:**Error exponent analysis of MIMO Channels with progressive scattering

**Speaker:**Giusi Alfano (Politecnico di Torino)

**Date:**Mittwoch, 15. April 2015, 11:15 Uhr

**Room:**Seminarraum C208, Steyrergasse 30/II

**Abstract:**

Several wireless communications settings can be suitably modeled by products of random matrices. This talk is focused on finite-dimensional analysis of multiple-antenna channels with progressive scattering. The trade-off between communication reliability (error probability at the receiver) and the required information coding length, at communication rates below the channel capacity, is investigated. Dependence of this trade-off performance index, usually referred to as ``error exponent'', on the singular values and singular vectors of the product of Ginibre matrices is unveiled. The relationship between the error exponent and the Cauchy transform of the channel matrix (grammian) is illustrated. Some open problems in the field are listed.

#### Strukturtheorie-Seminar

**Title:**Universal properties of harmonic functions on trees

**Speaker:**Evgueni Abakoumov (Université Paris-Est Marne-la-Vallée)

**Date:**Donnerstag, 26. März 2015, 14:15 Uhr

**Room:**Seminarraum C208, Steyrergasse 30/III

**Abstract:**

#### TERMINAENDERUNG: FoE-Kolloquium

**Title:**Bits, Codes, Entropy and Information

**Speaker:**Gerhard Kramer (TU München)

**Date:**Mittwoch 25.3.2015, 16:00 (Kaffeepause), 16:30 (Vortrag)

**Room:**Hörsaal i1, Inffeldgasse 18

**Abstract:**

The talk explains the meaning of entropy from the perspective of

information theory. The concept of ``information'' is described, and the

ideas are applied to three problems: data compression, secrecy

communication, and error correction. Finally, we describe the applicability

of ``codes'' to network problems, including network coding and relay

transmission.

Gerhard Kramer ist Alexander von Humboldt Professor an der TU München, war

Vorsitzender der IEEE Information Theory Society, und ist ein

IEEE Fellow und IEEE Distinguished Lecturer.

#### Gastvortrag

**Title:**A homologically persistent skeleton in computer vision

**Speaker:**Vitalyi Kurlin (Durham University)

**Date:**24.3.2015, 10:00

**Room:**Seminarraum 2, Institut f. Geometrie

**Abstract:**

2D images often contain irregular salient features and interest points with

non-integer coordinates. Our skeletonization problem for such a noisy sparse

cloud is to summarize the topology of a given 2D cloud across all scales in

the form of a graph, which can be used for combining local features into a

more powerful object-wide descriptor. We extend a classical Minimum Spanning

Tree of a cloud to the new fundamental concept of a Homologically Persistent

Skeleton, which is scale-and-rotation invariant and depends only on the

given cloud without extra parameters. This graph

(1) is computable in time $O(n \log n)$ for any $n$ points in the plane;

(2) has the minimum total length among all graphs that span a 2D cloud at

any scale and also have most persistent 1-dimensional cycles;

(3) is geometrically stable for noisy samples around planar grahs.

{\it References:} http://kurlin.org/projects/homologically-persistent-skeleton-dim2.pdf}

**Title:**Colloquium on Harmonic Analysis and Discrepancy Theory

**Speaker:**Peter Grabner, Florian Pausinger, Luca Brandolini, Michael Drmota, Gerhard Larcher, Giancarlo Travaglini, Leonardo Colzani, Giacomo Gigante ()

**Date:**19.-20. März 2015

**Room:**Seminarraum C208, Seminarraum 2 Geometrie.

**Abstract:**

**Program**

**Thursday, March 19, 2015**

*Place*: Seminarraum C208, Mathematik, Steyrergasse 30/2, TU Graz

16:00: Peter Grabner (TU Graz)

*Distributing many points on spheres: minimal energy and designs*

16:45: Florian Pausinger (IST Austria)

*On a family of multidimensional variations*

17:30: Luca Brandolini (Univ. Bergamo, Italy)

*Approximation of integrals in metric measure spaces*

**Friday, March 20, 2015**

*Place*: Seminarraum 2 Geometrie, Kopernikusgasse 24/4, TU Graz

(under the frame of the DK Discrete Mathematics)

10:30: Michael Drmota (TU Wien)

*Quasi-Random properties of the Thue-Morse sequence and related
problems*

11:00: Gerhard Larcher (Univ. Linz)

*Analysis of lacunary trigonometric products and discrepancy of*

sequences in the unit interval

sequences in the unit interval

*Place*: Seminarraum C208, Mathematik, Steyrergasse 30/2, TU Graz

14:00: Giancarlo Travaglini (Univ. Milano, Italy)

*Decay of Fourier transforms and L2 discrepancy*

14:45: Leonardo Colzani (Univ. Milano, Italy)

*L(p) and Weak-L(p) estimates for the number of integer points in translated domains*

15:30: Giacomo Gigante (Univ. Bergamo, Italy)

*Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus*

\newpage

**Abstracts**

**Florian Pausinger**, IST Austria,

*On a family of multidimensional variations*

Motivated by recent ideas of Harman, we introduce a new concept of variation of multi-dimensional functions yielding a general version of the Theorem of Koksma-Hlawka. One strength of our approach is that the corresponding spaces of functions of bounded variation have nice properties and include various discontinuous functions in a natural way.

Furthermore, our general framework is shown to bring together dierent classical notions of variation. We illustrate our results on concrete integration problems from integral geometry and stereology.

This is a joint work with Anne Marie Svane.[2em]

**Michael Drmota**, TU Wien.

*Quasi-Random properties of the Thue-Morse sequence and related problems*

Thue-Morse sequence that can be defined by $t_n = s(n)$ mod 2, where $s(n)$ denotes the binary sum-of-digits function, has been studied in many different contexts from combinatorics to algebra, number theory, harmonic analysis, geometry and dynamical systems. For example, it has a linear subword complexity and is almost periodic.

It is also one of the easiest examples of a non-trivial automatic sequence, that is, a sequence that is the output of a finite automaton, where theinput are the q-ary digits of a positive integer.

Since the subword complexity of the Thue-Morse sequence is linear (as for all automatic sequences) the entropy of the related dynamical system is zero. This also means that is does not behave like a random sequence. However, the situation changes drastically when one uses proper subsequences of automatic sequences, for example the subsequence along primes or squares. It is conjectured that the resulting sequences are normal sequences so that they

are "random". Recently this property was proved (together with C. Mauduit and J. Rivat) for the Thue-Morse sequence along the subsequence of squares.

The purpose of this talk is give an overview of this field of research

and to present the key techniques for obtaining distributional results.

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Functional calculus for definitizable self-adjoint linear relations on Krein spaces

**Speaker:**Prof. Dr. Michael Kaltenbäck (TU Wien)

**Date:**19.3.2015, 15:00 Uhr

**Room:**C307

**Abstract:**

We are going to introduce a functional calculus $\phi \mapsto \phi(A)$ for self-adjoint definitizable linear relations $A$ on Krein spaces. This functional calculus is the proper analogue of $\phi \mapsto \int \phi \, dE$ in the Hilbert space situation. It also comprises the Spectral Theorem for self-adjoint definitizable operators -- developed by Heinz Langer -- on Krein spaces showing the existence of spectral projections. This work relys on some sort of transformation of linear relations and uses ideas going back to Peter Jonas, Michael Dritschel and James Rovnyak.

#### Strukturtheorie-Seminar

**Title:**Rotor-routing on Galton-Watson trees

**Speaker:**Sebastian Müller (Université d'Aix-Marseille und TU Graz)

**Date:**Donnerstag, 19. März 2015, 11:15 Uhr

**Room:**Seminarraum C307, Steyrergasse 30/III

**Abstract:**

A rotor-router walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then is routed to the neighbor the rotor is now pointing at. In the talk we discuss the behavior of rotor-router walks on Galton-Watson trees and give a classification in recurrence and transience for transfinite rotor-router walks on these trees. (joint work with W. Huss and E. Sava-Huss)

#### Vortrag im Seminar Optimierung und Diskrete Mathematik

**Title:**Maximum Persistency in Energy Minimization

**Speaker:**Alexander Shekhovtsov (ICG, TU Graz)

**Date:**17.3. 2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

The talk addresses combinatorial problems that can be formulated as

minimization of a partially separable function of discrete variables.

This includes such problems as vertex packing, pseudo-Boolean

optimization, 0-1 polynomial programming, weighted constraint

satisfaction and energy minimization in graphical models.

For polyhedral relaxations of these problems it is generally not true

that variables which are integer in the relaxed solution will retain the same

values in an optimal discrete solution. Those which do are called

persistent. Such persistent variables define a part of a globally

optimal solution. Once identified, they can be excluded from the

problem, reducing its size.

In this talk I pose the problem of determining the maximum subset of

persistent variables identifiable from a linear relaxation. Since

deciding whether a given partial assignment is globally optimal is

NP-hard, a tractable persistency technique has to be based on

tractable sufficient conditions. Different sufficient conditions were

proposed in computer vision, bioinformatics and discrete optimization.

A generalized sufficient condition is introduced which builds on a

given polyhedral relaxation. It turns out that the maximum persistent

subset qualifying this sufficient condition can be found in polynomial

time for any polyhedral relaxation. This maximum provides a provably

larger reduction of the problem than ad hoc or optimizing techniques

based on weaker conditions.

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**The order problem for Hamburger Hamiltonians

**Speaker:**Prof. Dr. Harald Woracek (TU Wien)

**Date:**13.3.2015, 14:00 Uhr

**Room:**C307

**Abstract:**

Let $H$ be a trace-normed positive semidefinite $2$-dimensional Hamiltonian on a finite

interval $[0,L]$, and let $W(x,z)$, $x\in[0,L]$, be the fundamental solution of the canonical

system with Hamiltonian $H$. Then the entries $w_{ij}(L,z)$ of $W(L,z)$ are entire functions of the Cartwright class.

All the four functions have the same exponential type which is given by the Krein-de~Branges formula

\[

\text{exponential type of }w_{ij}(L,.)=\int_0^L\sqrt{\det H(x)}\,dx

.

\]

If $\det H(x)=0$, $x\in[0,L]$ a.e., the order of $w_{ij}(L,.)$ may be less than $1$.

It is known that the functions $w_{ij}(L,.)$, $i,j=1,2$, have the same order, call it $\rho(H)$, and that

for arbitrary $\rho\in[0,1]$ there exist Hamiltonians $H$ with $\det H=0$ a.e.\ and $\rho(H)=\rho$.

A problem that arises naturally is to determine or estimate $\rho(H)$ for given $H$.

The -- probably -- first result dealing with growth properties different from exponential type is due to M.S. Liv\v{s}ic back in 1939.

Liv\v{s}ic shows that the order of the four entire functions involved in the Nevanlinna parameterisation corresponding to an

indeterminate (Hamburger-) moment sequence $(s_n)_{n=0}^\infty$ is not less than the order of the entire function

$\sum_{n=0}^\infty\frac{z^{2n}}{s_{2n}}$.

Whether or not these orders always coincide remained an open problem ever since the work of Liv\v{s}ic.

We consider Hamiltonians corresponding to indeterminate power moment problems, i.e., which consist of a sequence of

indivisible intervals accumulating only at $L$. Following I.S. Kac we call them Hamburger Hamiltonians.

It is shown in recent work of C. Berg and R. Szwarc that for such Hamiltonians $\rho(H)$ can be computed in terms

of the coefficients of orthogonal polynomials (all coefficients are involved).

Clearly, this formula is nearly impossible to apply since the orthogonal polynomials can be fully computed only in

some sporadic cases when knowledge about special functions can be employed.

In this talk we present:

(i) An upper estimate for $\rho(H)$ which is explicit in terms of the Hamiltonian (lengths and angle of the indivisible intervals)

(ii) A lower estimate which can be deduced from the Berg-Szwarc formula (or, probably simpler, be proven directly).

(iii) A regularity condition on the lengths and angles which ensures that these estimates coincide and hence establish a formula for $\rho(H)$ which is explicit in terms of lengths and angles;

the message is that the faster lengths decay and the smoother angles vary, the smaller $\rho(H)$ will be.

(iv) Examples which show that dropping regularity can lead to situations where both estimates do not coincide with $\rho(H)$.

In particular, we show that in Liv\v{s}ic's Theorem equality does not always hold.

The talk is based on joint work with Raphael Pruckner and Roman Romanov.

#### Zahlentheoretisches Kolloquium

**Title:**$n$-universal sets in number fields

**Speaker:**Anna Szumowicz (Jagiellonian University Krak\'ow)

**Date:**Freitag, 13. 3. 2015, 15 Uhr

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

Abstract:

Let $K$ be a number field and $\mathcal{O}_{K}$ be the ring of integers in

$K$. Let $p_{n}$ be the set of polynomials in $K[x]$ of degree at most $n$. We

say that a subset $S$ of $K$ is $n$-universal if for every $f$ in $p_{n}$ $f(S)\subset\mathcal{O}_{K}$ implies $f(\mathcal{O}_{K})\subset \mathcal{O}_{K}$. In the case of the rationals it is easy to show that the set $\{0,\cdots ,n\}$ is an example of an $n$-universal set. Moreover using Lagrange interpolation it can be proven that any $n$-universal set has at least $n+1$ elements (this is true in an arbitrary number field). V.V. Volkov, F.V. Petrov in [1] showed in $\mathbf{Q}[\char105]$ there are no $n$-universal set with $n+1$ elements for $n$ large enough and conjectured that the size of a minimal $n$-universal set is of order $\frac{\pi}{2}n + o(n)$.

During my talk I will present a joint work with Jakub Byszewski and Miko\l aj Fr\c aczyk in which we showed that there are no $n$-universal sets with $n+1$ elements if $K$ is an imaginary quadratic field (for $n$ large enough). Moreover we show the construction of $n$-universal set with $n+2$ elements in an arbitrary number field.

[1] On the interpolation of integer-valued polynomials, V.V. Volkov, F.V.

Petrov, Journal of Number Theory 133 (2013) 4224-4232.

#### Zahlentheoretisches Kolloquium

**Title:**Some results on polynomial Diophantine m-tuples

**Speaker:**Dr. Alan Filipin (University of Zagreb)

**Date:**Freitag, 13. 3. 2015, 14:15 Uhr

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

#### Vortrag

**Title:**Binary classification in high dimension using robust sparse PLS

**Speaker:**Peter Filzmoser (Institute of Statistics & Mathematical Methods in Economics, TU Wien)

**Date:**20. März 2015, 11.00 Uhr

**Room:**SR für Statistik (NT03098), Kopernikusgasse 24/III

**Abstract:**

Partial Robust M-regression (PRM) (Serneels et al., 2005) and Sparse Partial Robust M-regression (SPRM) (Serneels et al., 2014) are Partial Least Squares (PLS) alike robust regression methods which reduce dimensionality of the data by projection to latent structures. These methods inherit the advantages of PLS: They are applicable to high dimensional data with multicollinearities, and results can be visualized in biplots. Further SPRM performs intrinsic variable selection and obtains a sparse version of the latent variables, which can increase model precision when uninformative variables are present and cilitates the interpretation of the results.

Research has shown that PLS regression methods can be adapted for discriminant analysis (Barker & Rayens, 2003). We introduce two classification methods for binary response based on PRM and SPRM as robust alternatives to PLS discriminant analysis. PLS related algorithms for the estimation of latent variable models in classification problems are discussed and different approaches for outlier detection are presented. Theoretical considerations about

between-class variance and the decision boundaries motivate the construction of the algorithms. Further they are evaluated based on simulation studies, where the effect of outliers in the predictor space, wrong class labels in the response, uninformative variables and unequal group size is investigated. Thereunto, the number of components and the sparsity parameter are tuned via k-fold cross validation. In the simulation study and for real data examples from

mass spectrometry the performance of the methods is illustrated by misclassification rates and compared to non-robust counterparts.

References

Serneels, S. & Croux, C. & Filzmoser, P. & Van Espen, P.J. (2005). Partial robust M-regression.

Chemometrics and Intelligent Laboratory Systems, 79, 55â€“64.

Serneels, S. & Filzmoser, P. & Hoffmann, I. & Croux, C. (2014). Sparse partial robust

M-regression. ICORS14 Conference Guide & Book of Abstracts, 24.

Barker, M. & Rayens, W. (2003). Partial least squares for discrimination. Journal of

Chemometrics, 17, 166â€“173.

#### Strukturtheorie-Seminar

**Title:**An approach to Cerny's conjecture via the Wedderburn-Artin Theory

**Speaker:**Emanuele Rodaro (Universidade do Porto)

**Date:**Dienstag, 24. Februar 2015, 11:00 Uhr

**Room:**Seminarraum C307, Steyrergasse 30/III

**Abstract:**

Cerny's conjecture is one of the most longstanding open problems in the theory of finite automata (stated by Cerny in 1964). This conjecture claims that a deterministic finite automaton with $n$ states and synchronizing, has always a synchronizing word of length $(n-1)^{2}$.

In this seminar, I am going to show an approach to Cerny's conjecture using the Wedderburn-Artin theory. First I introduce the notion of a radical ideal of a synchronizing automaton, and then the natural notion of semisimple synchronizing automata. Semisimplicity gives the advantage of ``factorizing'' the problem of finding a synchronizing word into the sub-problems of finding words that are zeros into the projections of the simple components in the Wedderburn-Artin decomposition. This situation is applied to prove that Cerny's conjecture holds for the class of strongly semisimple synchronizing automata: these are the automata whose sets of synchronizing words are cyclic ideals, or equivalently are ideal regular languages which are closed by takings roots. (This is a work in progress with J. Almeida)

#### Vortrag im Seminar Optimierung und Diskrete Mathematik

**Title:**Solution Approaches for Double and Multi Row Facility Layout Problems

**Speaker:**Anja Fischer (TU Dortmund)

**Date:**10.2.2015, 16:00

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

Given a set of departments the Multi Row Facility Layout Problem (MRFLP) ask for a non-overlapping arrangement of the departments in a given number of rows such that the weighted sum of the pairwise center-to-center distances is minimized. In general, the lengths of the departments may vary, but we also consider the so called equidistant case when all lengths are equal to one. The MRFLP is an extension of the Linear Arrangement Problem (LA) as well as of the Single Row Facility Layout Problem (SRFLP). In contrast to these two problems, there might be spaces between neighboring departments in the same row in the MRFLP. In this talk we present two new models for the equidistant MRFLP that are based on results on the structure of optimal solutions. The first model uses binary betweenness variables as well as binary variables indicating whether two departments are in same position. The second model leads to a semidefinite programming relaxation which is solved using a spectral bundle method.

In the second part of the talk we present combinatorial lower bounds for the general MRFLP that are related to the so called star-inequalities of the LA and to approximation algorithms in parallel machine scheduling. Furthermore we study connections between (optimal) solutions of SRFLP and MRFLP.

Joint work with Miguel Anjos, Frank Fischer and Philipp Hungerländer

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**The cost of distinguishing graphs

**Speaker:**Wilfried Imrich (Montanuniversität Leoben)

**Date:**Dienstag 3.2.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

In a graph a set of vertices that is stabilized setwise by only the trivial automorphism is called a distinguishing class. Not every graph has such a set, but if it does, we call its minimum size the distinguishing cost. Many families of graphs have such sets, and for some families the distinguishing costs are surprisingly small.

The talk begins with a survey of results about about the distinguishing cost for finite and infinite graphs. Then it concentrates on infinite graphs with finite cost and new bounds on the distinguishing cost of graphs with linear growth, two ends and either infinite automorphism group, or finite group with infinite motion. There remain interesting, unresolved problems.

**Title:**Dr. School Seminar

**Speaker:**()

**Date:**30.1.2015, 13-14 Uhr

**Room:**Seminarraum 2, Inst. f. Geometrie

**Abstract:**

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Drawings of stack triangulations in the plane

**Speaker:**Thomas Selig (Universit\'e Bordeaux)

**Date:**Dienstag 27.1.2015, 14:15

**Room:**Seminarraum C208, Steyrergasse 30, 2. Stock

**Abstract:**

Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or ``draw'' these random stack triangulations in the plane $\mathbb{R}^2$ and study the asymptotic properties of these drawings, viewed as random compact metric spaces. We also look at the occupation measure of the vertices, and show that for these two distributions it converges to some random limit measure. The key ingredient is an encoding of the combinatorial structure of stack triangulations by ternary trees, which we enrich to obtain the relevant additional geometric information.

#### Kolloquium

**Title:**Computational Topology and Geometry

**Speaker:**()

**Date:**23.1.2015, 9-10:30, 13:30-14:30

**Room:**

**Abstract:**

#### Kolloquium

**Title:**Computational Topology and Geometry

**Speaker:**()

**Date:**22.1.2015, 9:30-11, 13:30-15:00

**Room:**

**Abstract:**

#### Vortrag

**Title:**Topological data analysis, the new frontier.

**Speaker:**Pawe{\l} D{\l}otko (Univ. Pennsylvania)

**Date:**Thursday 22.1.2015, 17:00

**Room:**Seminarraum Mechanik, Kopernikusgasse 24/IV

**Abstract:**

Computational topology has became an important tool in the applied

science. Until now its state of the art methods allowed to construct a

filtered simplicial or cubical complexes and to compute persistence

diagrams by using matrix reduction methods. All the computations were

made on a single computer with only very basic parallel methods. There

was no way to do a statistical analysis of larger families of results.

Still, this basic scheme has already provided very good results and a

further development of the filed is currently taking place. In this

talk I will present two directions of my research aiming in further

development of the TDA.

Firstly I will address the problem of scaling up the computations we

are able to perform by using a divide and conquer scheme to compute

homology and persistent homology in a distributed way. To achieve this

aim, I will introduce a Discrete Morse theory and show how one can

minimize a Discrete Morse complex preserving its (persistent)

homology. By using those concepts, a distributed algorithm to compute

persistence will be introduced. An application of the discussed scheme

in the analysis of fluid dynamics will be shown.

Secondly I will present a theory and a software toolbox to do basic

statistical operations on persistence diagrams. I will show how to

compute averages, standard deviations and distances between

persistence diagrams and how to make a practical use out of them.

#### Seminarvortrag

**Title:**A minimum area homology metric for similarity of curves on surfaces

**Speaker:**Mikael Vejdemo-Johansson (KTH -- Royal Institute of Technology, Stockholm)

**Date:**22.1.2015, 10:30 Uhr

**Room:**ID02104, Inffeldgasse 16c/II (Seminarraum Inst. CGV)

**Abstract:**

This presentation is based on the paper:

Computer Graphics Forum ({\tt http://dx.doi.org/10.1111/cgf.12514}): Computing minimum area homologies, by Erin Chambers and Mikael Vejdemo-Johansson.

Given two curves on a surface, or more generally two submanifolds of a manifold, one may ask for similarity measures between them. Such measures are useful for a variety of tasks, and have been constructed using Haussdorff metrics or Fréchet distances.

The Fréchet distances can be viewed as measuring the {\it width} of a homotopy between the curves, and this has driven some generalization work that include s the underlying topology into the measure itself. Dually, one might study the {\it height} of a homotopy between the curves. In both these cases, complexity for an exact computation turn out to be disadvantageous, though there have been efficient approximation algorithms.

In 2013, Chambers and Wang proposed a new approach, measuring the {\it area} of a connecting homotopy, and produced an algorithm with a reasonably fast complexity O($n\log n + I^2\log I$) for input curve complexity $n$, intersection count $I$).

Jointly with Chambers, I have proposed an approximation to the homotopy area metric that works with homology instead of homotopy. We produce bounds for error in area computation, and demonstrate that the computational complexity of the homology computation reduce to well known and highly optimized linear programming and optimization problems. Our methods generalize smoothly to arbitrary-dimensional submanifolds of arbitrary-dimensional cell decompositions.

#### Kolloquium

**Title:**Computational Topology and Geometry

**Speaker:**()

**Date:**21.1.2015, 9-10:30, 13:30-15:00

**Room:**

**Abstract:**

#### Kolloquium

**Title:**Computational Topology and Geometry

**Speaker:**()

**Date:**20.1.2015, 9-10:30, 13-14:30, 16-17:30

**Room:**

**Abstract:**

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Boundary triplet approach and tensor products

**Speaker:**Dr. Hagen Neidhardt (WIAS Berlin)

**Date:**29.1.2015, 14:15 Uhr

**Room:**C307

**Abstract:**

The boundary triplet approach is applied to symmetric operators of the form $$S = A \otimes I_T + I_A \otimes T$$ where the operator $A$ is symmetric and the operator $T$ is self-adjoint and in general unbounded. It is assumed that a boundary triplet for $A$ is given. Using that a boundary triplet for $S$ is constructed. Moreover, the gamma field and Weyl function are computed. Finally, applications are given.

#### Gastvortrag

**Title:**Under Pressure

**Speaker:**Adrian Dumitrescu (University of Wisconsin--Milwaukee)

**Date:**19.1.2015, 15:00

**Room:**Seminarraum IGI, Inffeldgasse 16b, 1.Stock (Raum Nr. IC01074)

**Abstract:**

According to the ideal gas law in thermodynamics, $ P V = N k T, $ where $P$~is the absolute pressure of the gas measured in atmospheres; $V$ is the volume expressed in liters, $N$ is the number of particles in the gas, $k$ is Boltzmann's constant relating temperature and energy; and $T$ is the absolute temperature in kelvins. In particular, at a constant temperature, $P_1 V_1 =P_2 V_2 =$ constant.

The technique of exerting pressure is also frequently used in geometry, particularly in geometric constructions (although it is never explicitly mentioned). We present a few illustrations.

We start with a construction of J. Pach and G. T\'oth, from 1996, involving coin graphs, in relation with a problem of Erd\H{o}s (1983). We then review a construction of Ajtai from 1973 involving squares, in relation with a problem of T. Rado (1928). We further continue with some constructions of our own:

skip

-- a construction involving squares (from 2008,

joint work with S. Bereg and M. Jiang), in relation with

Rado's problem, and

skip

-- a construction involving disks (from 2012, joint work with M. Jiang), in relation with a problem of Hosono and Urabe (2011).

#### Mathematisches Kolloquium

**Title:**Optimal transport and stochastic portfolio theory

**Speaker:**Prof. Dr. Walter Schachermayer (Universität Wien)

**Date:**Freitag, 16. 1. 2015, 15.30 Uhr (15:00 Kaffeepause am Institut f. Statistik)

**Room:**SR Statistik, Kopernikusgasse 24, 3.OG

**Abstract:**

In a recent paper S. Pal and T. Wong established a remarkable connection

between the the following two notions. On the one hand functionally generated

portfolios as introduced by R. Fernholz some fifteen years ago. On the other

hand a multiplicative version of the concept of cyclical monotonicity. We shall

try to discuss and motivate the underlying ideas.

#### Advanced Topics in Discrete Mathematics

**Title:**101 extremal properties of greedy trees

**Speaker:**Stephan Wagner (Stellenbosch University)

**Date:**Freitag, 16.1.2015, 10:30 (Kaffee/Tee ab 10:00)

**Room:**Seminarraum 2 Geometrie, 4. Stock, Kopernikusgasse 24

**Abstract:**

#### Colloquium on Graph Theory - Erinnerung

**Title:**

**Speaker:**Prof. Dr. T. Doslic, Dr. S. Majstorovic (Croatia)

**Date:**Donnerstag, 15.1.2015, 14:15 Uhr

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

{\bf Prof. Dr. Tomislav Doslic}, Zagreb[0.2cm]

Title: {\bf On some structural and enumerative aspects of maximal matchings}[0.5cm]

Abstract: A matching M of a graph G is maximum if no other matching in G has more edges than M; a matching M is maximal if no other matching of G contains

M as a proper subset. Maximal matchings are much less researched and less

understood than the maximum ones. We present results on some structural

and enumerative properties of maximal matchings in several classes of

chemically relevant graphs.[0.5cm]

{\bf Dr. Snjezana Majstorovic}, Osijek[0.2cm]

Title: {\bf Indivisible graphs}[0.5cm]

Abstract: In the study of complex networks, community structure refers to

the occurrence of groups of nodes in a network that are more densely

connected internally than with the rest of the network.

One of the most popular community detection methods is the Newman’s

spectral modularity maximization algorithm, which divides a graph into two

communities based on the signs of the principal eigenvector of its

modularity matrix in the case that the modularity matrix has positive

largest eigenvalue. Newman defined a graph to be indivisible if its

modularity matrix has no positive eigenvalues. In this lecture, a

characterization of indivisible graphs is given.

#### Seminar Angewandte Analysis und Numerische Mathematik

**Title:**Sectorial forms and degenerate operators

**Speaker:**Prof. Dr. Tom ter Elst (University of Auckland)

**Date:**22.1.2015, 14 Uhr c.t.

**Room:**C307

**Abstract:**

In the theory of sectorial forms and holomorphic semigroups

a basic assumption is that the form is closed, or at least

closable. This is a nasty difficult condition. In a recent

paper with Wolfgang Arendt we proved that one can associate

in a natural way a holomorphic semigroup generator to any

sectorial form, even if it is not closable. Thus one can

forget closability. This opens the door to consider complex

degenerate elliptic differential operators without demanding

that they are symmetric or strongly elliptic. In the talk we

present several examples and applications.

#### Zahlentheoretisches Kolloquium

**Title:**Complexity of Banach space valued integration

**Speaker:**Prof. Dr. Aicke Hinrichs (Johannes Kepler Universität, Linz)

**Date:**Freitag, 9. 1. 2015, 14.15 Uhr

**Room:**Seminarraum C 208, 2. Stock, Steyrergasse 30, TU Graz

**Abstract:**

We study the complexity of Banach space valued integration problems in the randomized setting. We explain the interplay between the geometry of the underlying Banach space and the rate of the nn-th minimal errors. The relevant notion of Banach space geometry is the Rademacher type of the space. We also explain the motivation which comes from applications to the complexity of definite and indefinite integration and to the solution of ODEs. This is joint work with Stefan Heinrich.