### 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.