### Talks in 2013

#### Mathematisches Kolloquium

**Title:**Quantum graphs and networks

**Speaker:**Pavel Exner (Czech Academy of Sciences)

**Date:**17.12.2013, 15:30 Kaffee im Foyer, 16:00 Vortrag

**Room:**Hörsaal BE01

**Abstract:**

Dynamics of a quantum particle confined to a graph is interesting both

mathematically and physically. The corresponding self-adjoint Hamiltonians

typically contain free parameters coming from coupling of the wave

functions at the graph vertices. It is a longstanding problem whether one

can motivate the parameter choice by approximating the graph Hamiltonian

by operators on a family of networks, i.e. systems of tubular manifolds

the transverse size of which tends to zero. It appears that the answer

depends on the conditions imposed on tube boundaries. In this talk we

present a complete solution for Neumann networks: we demonstrate that

adding properly scaled potentials and changing locally the topology, one

can approximate any admissible vertex coupling. The result comes from a

common work with Taksu Cheon, Olaf Post, and Ond\v{r}ej Turek.

#### Gastvortrag

**Title:**Verspielte Mathematik

**Speaker:**Alexander Mehlmann (TU Wien)

**Date:**13.12.2013, 14 Uhr

**Room:**Seminarraum 2, Kopernikusgasse 24

**Abstract:**

\sloppy

Trotz der zweifellos vorhandenen Bezugspunkte zur den schönen Künsten scheint die moderne Mathematik manchmal davor zurückzuscheuen, sich auf das Spiel mit literarischen Mustern einzulassen. Dieses spröde Verhalten der ernsthaftesten aller Musen entspricht jedoch keineswegs ihrer ursprünglichen Zielsetzung.

Für die Mathematiker Antonio Manetti (1423--1497) und Galileo Galilei (1564--1642) war die Beschäftigung mit Dantes ``Divina Commedia'' ein selbstverständlicher Schritt im Dienste der Dichtkunst und nicht zuletzt auch ein entscheidender zur Stärkung der eigenen Reputation. Beiden verdanken wir erstaunliche geometrische Einsichten in der Hölle Maß und Dimensionen; ein wahrhaft meisterlicher Ba\-lance\-akt zwischen den Erfordernissen diesseitiger Geodäsie und den Dogmen jenseitsgewandter Theologie.

Die rhetorische Tradition, Mathematik in Verse zu fassen, lässt sich unter anderem am Epigramm des Erzgrüblers Archimedes zum Problem der Rinder des Sonnengottes entdecken und nicht zuletzt durch Tartaglias poetische Formel zur Lösung der kubischen Gleichung bekräftigen.

Im Vortrag zur ``Verspielten Mathematik'' werden unter anderem Modelle der Spieltheorie vorgestellt, die eine durchaus adäquate, wenn auch augenzwinkernde, Beschreibung literarischer Motive zulassen. Kann sie einer derartig wohltemperierten, mathematischen Partitur folgen, so erweist sich die sogenannte ``Königin der Wissenschaften'' durchaus als ein geeignetes Instrument, um der Literatur interessante Noten abzugewinnen. Durch die Linse der Mathematik betrachtet, strebt der Mythos vom Wahnsinn des Odysseus einer überraschend anderen Lösung zu und selbst Goethes Faust öffnet sich durch eine spieltheoretische Modellierung der Teufelswette einer endgültigen Klärung der paradoxen Rettung Faustens.

#### Advanced Topics in Discrete Mathematics

**Title:**Diophantine approximation, flows on homogeneous spaces and counting

**Speaker:**Martin Widmer (Royal Holloway University, London)

**Date:**Friday 13. Dec. 2013, 10:30

**Room:**Seminar Room 2 of the Geometry Institute, Kopernikusgasse 23/4

**Abstract:**

After a very gentle introduction to Diophantine approximation we shall explain

what approximation properties of real numbers by rationals have to do with

flows on homogenous spaces, and how the latter can be used to prove some new

counting results on the number of "good" rational approximations to a given

irrational real number.

#### Zahlentheoretisches Kolloquium

**Title:**On Stolarsky's second problem : Mean value of the sum of digits of polynomial values

**Speaker:**Prof.Dr.Thomas Stoll (Université de Lorraine, Nancy, dzt. TU Graz)

**Date:**Mittwoch, 11. 12. 2013, 16:30 Uhr, s.t.

**Room:**Seminarraum A306, TU Graz, Steyrerg.30, 3.Stock, Geodäsie

**Abstract:**

Abstract: In this talk we present our recent resolution of a problem of

Stolarsky (1978) about the mean value of the sum of digits of polynomial

values in simultaneous digital expansions. The proof uses probabilistic

tools such as a result due to Bassily/Katai, and Cesaro means. Joint

work with M. Madritsch.

#### Doctoral Day

**Title:**Doctoral School Seminar

**Speaker:**M. Raseta, A. Bazarova, R. Rissner, C. Kühn ()

**Date:**6.12.2013, 10:30-13:00

**Room:**Seminarraum 2, Kopernikusgasse 24

**Abstract:**

10:30 M. Raseta

11:00 A. Bazarova

11:30 Lunch Break

12:00 R. Rissner

12:30 C. Kühn

#### Gastvortrag

**Title:**Direct sums of trace maps and self-adjoint extensions

**Speaker:**Prof. Dr. Andrea Posilicano (University of Insumbria)

**Date:**2.12.2013, 16:00 Uhr

**Room:**C 307

**Abstract:**

We give a simple criterion so that a direct sum of trace (evaluation) maps is a trace map.

An application to the theory of self-adjoint extensions of direct sums of symmetric operators is provided;

this gives an alternative approach to results recently obtained by Malamud-Neidhardt and Kostenko-Malamud

using regularized direct sums of boundary triplets. An example regarding the Laplace-Beltrami operator on

conic-type surfaces with singular/degenerate Riemannian metrics is presented.

#### Gastvortrag

**Title:**No Free Form

**Speaker:**Michael Eigensatz (Evolute)

**Date:**29.11.2013, 14:00

**Room:**Seminarraum 2, Kopernikusgasse 24, 8010 Graz

**Abstract:**

Geometry is a central element for architectural expressiveness. Modern computer tools provide the illusion that we are free to design the most extraordinary geometry we can ever imagine. In the real world, however, geometry, like physics, follows rules and is constrained by inevitable mathematical truths. Therefore, a simple lesson from the field: To make extraordinary geometry work, one has to understand geometry. I will show some examples.

#### Zahlentheoretisches Kolloquium

**Title:**Prime spectra of certain two dimensional integral domains - history and new development

**Speaker:**Prof. Dr. Aihua Li (Montclair State University, USA)

**Date:**Freitag, 29. 11. 2013, 14:00, c.t.

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

**Abstract:**

Abstract:

For a commutative ring $R$, the spectrum, Spec$(R)$, is the partially ordered set of

the prime ideals of $R$ ordered by inclusion. This talk focuses on prime structure of

$\mathbb Z[x]$, the polynomial ring in one variable over the integers. It is known that several

types of Noetherian integral domains have their prime spectra order-isomorphic

to Spec$(\mathbb Z[x])$. In 1986, Roger Wiegand conjectured that every two-dimensional

integral domain which is a finitely generated $\mathbb Z$-algebra has prime spectrum orderisomorphic

to Spec$(\mathbb Z[x])$. This talk will give a history and recent development

about the conjecture and will introduce some newly developed results on graph

theory properties of Spec$(\mathbb Z[x]) \backslash \{0\}$ as a bipartite graph.

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

**Title:**Potential methods for Stokes and Brinkman systems of Lipschitz domains

**Speaker:**Prof. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Universität Stuttgart)

**Date:**28.11.2013, 16:00 Uhr

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

**Abstract:**

The lecture consists of two parts. In the firt part we use the method of matched asymptotic expansions for the two-dimensional steady flow of a viscous incompressible fluid at low Reynolds number past a porous body of arbitrary shape. We assume that the flow inside the porous body is modeled by the continuity and the Brinkman equations, and that the velocity and boundary traction fields are weakly continuous across the interface between the fluid and the porous medium. By employing indirect boundary integral representations, the problem is reduced to uniquely solvable systems of Fredholm integral equations of the second kind in some Sobolev spaces. It is shown that the flow and also the force exerted by the exterior flow on the porous body admit an asymptotic expansion with respect to low Reynolds number, whose terms depend on the solutions of the above mentioned systems of boundary integral equations. By using the Oseen flow in the exterior, it can be shown that the Stokes–Brinkman expansion converges in any compact region to the Oseen–Brinkman solution if the Reynolds number tends to zero, in a similar manner as shown by G.C. Hsiao and R.C. MacCamy in 1973 and 1982 for flows around rigid obstacles. In the second part we study boundary value problems of Robin type for the semilinear elliptic Darcy–Forchheimer–Brinkman system on Lipschitz domains. We use a layer potential analysis and Schauder’s fixed point theorem to show the existence and uniquness of the solution on a bounded Lipschitz domain in Rn(n = 2 or 3) with small data in L2–Sobolev spaces.

#### Strukturtheorie-Seminar

**Title:**From trees to functions, and back

**Speaker:**Prof. Dr. Rudolf Grübel (Universität Hannover)

**Date:**Mittwoch, 27.11.2013, 11 Uhr c.t.

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

**Abstract:**

The famous Harris correspondence provides a very useful link between simply generated random trees and random functions on the unit interval. I will

-- describe two attempts (2009, 2014) to obtain an analogue for search trees,

-- discuss some current work, some of it joint with Steve Evans and Anton Wakolbinger, on the relation to ordered ultrametric spaces and IDLA models.

#### Strukturtheorie-Seminar

**Title:**Rate of convergence in the entropic free Central Limit Theorem

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

**Date:**Monday, 25.11.2013, 11 Uhr c.t.

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

**Abstract:**

We prove an expansion for densities in the free CLT and apply this

result to an expansion in the entropic free central limit theorem assuming a moment condition for the free summands.

#### Advanced Topics in Discrete Mathematics

**Title:**Counting lattice points, o-minimal structures and applications

**Speaker:**Fabrizio Barroero (TU Graz)

**Date:**Friday, 22. Nov. 2013, 10:30

**Room:**Seminar Room 2 of the Geometry Institute, Kopernikusgasse 23/4

**Abstract:**

#### Advanced Topics in Discrete Mathematics

**Title:**Good drawings and rotation systems of complete graphs

**Speaker:**Prof. Oswin Aichholzer (Institut für Softwaretechnologie, TU Graz)

**Date:**Freitag, 22. November 2013, 14:15 - 15:00

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

**Abstract:**

In a good drawing of a complete graph the vertices are drawn as distinct points in the plane, edges are drawn as non-self-intersecting continuous arcs connecting its two end points, but not passing through any other point representing a vertex. Moreover, any pair of edges intersects at most once, either in their interior or at a common endpoint, no tangencies are allowed and no three edges pass through a single crossing. These drawings are also called simple topological graphs.

A rotation system (of a good drawing of a complete graph) gives, for each

vertex v of the graph, the circular ordering around v of all edges incident to v. In combinatorics, rotation systems were first used by Hefner in 1891 to encode embeddings of graphs onto orientable surfaces, determining the genus. In the plane (or equivalently on the sphere) the rotation system of a good drawing does not fully determine the drawing, but contains combinatorial information like all pairs of edges which intersect.

We present basic properties of these two concepts, as well as recent progress. This includes results on the number of realizable rotation systems, the crossing number of complete graphs, the number of empty triangles, and relations to other systems like the order type of a point set.

#### Zahlentheoretisches Kolloquium

**Title:**Number theoretic problems in computer science

**Speaker:**Prof. Dr. Helmut Prodinger (Univ. of Stellenbosch, dzt. TU Graz)

**Date:**Mittwoch, 20. 11. 2013, 16:30 Uhr, s.t.

**Room:**Seminarraum A306, TU Graz, Steyrerg.30, 3.Stock, Geodäsie

**Abstract:**

Within a period of 35 years, the speaker has encountered numerous

appearences of number theoretic concepts. The simplest is about

Fibonacci numbers, also of graphs. Others include digital problems

which are related to the analysis of the register function, Batcher’s

odd-even merge, the Hamming weight of redundant representations and others.

The fascinating area of q-series is perhaps halfway between Combinatorics and

Number Theory. The talk will highlight a few things from this speaker’s practice;

no special knowledge is required.

#### Gastvortrag

**Title:**Lattice Polygons and Real Roots

**Speaker:**Michael Joswig (TU Berlin)

**Date:**Di 19.11.2013, 16:00

**Room:**Seminarraum 2, Inst. f. Geometrie, Kopernikusgasse 24

**Abstract:**

It is known from theorems of Bernstein, Kushnirenko and Khovanskii from the

1970s that the number of complex solutions of a system of multivariate

polynomial equations can be expressed in terms of subdivisions of the Newton

polytopes of the polynomials. For very special systems of polynomials

Soprunova and Sottile (2006) found an analogue for the number of real

solutions. In joint work with Ziegler we could give a simple combinatorial

formula and an elementary proof for the signature of foldable triangulation

of a lattice polygon. Via the Soprunova-Sottile result this translates into

lower bounds for the number of real roots of certain bivariate polynomial

systems.

#### Strukturtheorie-Seminar

**Title:**Percolation in hyperbolic space: the non-uniqueness phase

**Speaker:**Jan Czajkowski (Universität Wroclaw/TU Graz)

**Date:**Monday, 18.11.2013, 11 Uhr c.t.

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

**Abstract:**

I will talk on one part of my PhD thesis, which I am going to publish. I

consider Cayley graphs of reflection groups of finite-sided Coxeter polyhedra in the 3-dimensional hyperbolic space $H^3$, with the standard sets of generators. As main result, I prove the existence of a non-degenerate non-uniqueness phase of Bernoulli bond and site percolation on such graphs, i.e. that the critical probability is strictly less than the unification probability, for two classes of such polyhedra:

- for any polyhedra as above with at least 13 faces;

- for any compact right-angled polyhedra as above.

I also establish a natural lower bound for the growth rate of such Cayley

graphs (when the number of faces of the polyhedron is at least 6), used to prove the main result.

#### Gastvortrag

**Title:**Optimal adaptive estimation in nonparametric regression with one-sided errors

**Speaker:**Moritz Jirak (Institut für Mathematik, Humboldt-Universität zu Berlin)

**Date:**Freitag, 29. November 2013, 11.00 Uhr

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

**Abstract:**

We consider the model of non-regular nonparametric regression where smoothness constraints are imposed on the regression function and the regression errors are assumed to decay with some sharpness level at their endpoints. These conditions allow to improve the regular nonparametric convergence rates by using estimation procedures which are based on local extreme values rather than local averaging. We study this model under the realistic setting in which both the smoothness and the sharpness degree are unknown in advance. We construct adaptation procedures applying a nested version of Lepski's method and the negative Hill estimator which show no loss in the convergence rates with respect to the general $L_q$-risk and a logarithmic loss with respect to the pointwise risk. Optimality of these rates is proved. Some numerical simulations and an application to real data are provided.

#### Strukturtheorie-Seminar

**Title:**Synchronizing automata and approaches to the Cerny conjecture

**Speaker:**Dr. Emanuele Rodaro (Univ. Porto, Portugal)

**Date:**Montag, 11.11.2013, 11 Uhr c.t.

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

**Abstract:**

An automaton is called synchronizing if there is a word w and a state q such that w applied to an arbitrary state p leads to q. This notion naturally appears in different areas of computer science to model systems which are robust against errors. In this seminar we will survey some results on synchronizing automata and different problems related to them, and we will focus in particular on the longstanding Cerny conjecture and some approaches to tackle it.

#### Zahlentheoretisches Kolloquium

**Title:**Extremes of integral through the copulas

**Speaker:**Prof. Dr. Oto Strauch (Slovak Academy of Sciences)

**Date:**Mittwoch, 6.11.2013, 16:30 Uhr, s.t.

**Room:**Seminarraum A306, TU Graz, Steyrerg.30, 3.Stock, Geodäsie

**Abstract:**

In this note we discusse maximum or minimum

of the integral $\int_0^1\int_0^1F(x,y)\dd g(x,y)$,

where $g(x,y)$ goes through the copulas, i.e.,

distribution functions $g(x,y)$ satisfying $g(x,1)=x$ and $g(1,y)=y$.

$F(x,y)$ is an arbitrary continuous function on $[0,1]^2$.

The solution is known, if partial derivative

$\frac{\partial^2 F(x,y)}{\partial x\partial y}$ on $[0,1]^2$ has a constant

signum. For maximum we have $g(x,y)=\min(x,y)$ and for minimum

$g(x,y)=\max(x+y-1,0)$. Also there is known a method to compute

$g(x,y)$, if $[0,1]^2$ is divided on two parts $[0,1]\times[0,Y]$

and $[0,1]\times[Y,1]$ containing positive and negative signum

of $\frac{\partial^2F(x,y)}{\partial x\partial y}$, respectively.

All others is open, for example, if $[0,1]^2$ is divided on two

triangles by diagonal.

#### Zahlentheoretisches Kolloquium

**Title:**Monte Carlo integration in Hilbert space with reproducing kernel

**Speaker:**Prof. Dr. Vladimír Baláž (Slovak University of Technology)

**Date:**Mittwoch, 6.11.2013, 17:00 Uhr

**Room:**Seminarraum A306, TU Graz, Steyrerg.30, 3.Stock, Geodäsie

**Abstract:**

#### Strukturtheorie-Seminar

**Title:**Random walks with exotic spectral measure

**Speaker:**Łukasz Grabowski (University of Oxford)

**Date:**Thursday, 24.10.2013, 11:00 Uhr c.t.

**Room:**SR A306, Steyrergasse 30, 3. Stock, Geodäsietrakt

**Abstract:**

I will describe my recent work with B. Virag in which we exhibit random walk operators on various wreath products with interesting spectral properties: operators with singularly continuous spectra and operators with very large densities, but without atoms.

#### Gastvortrag

**Title:**Visualisierung -- Simulation -- Animation in der Mathematik

**Speaker:**Georg Glaeser (Univ. f. Angewandte Kunst, Wien)

**Date:**22.10.2013, 17:00 Uhr

**Room:**Seminarraum 2, Inst. f. Geometrie, Kopernikusgasse 24

**Abstract:**

Das Erstellen hochwertiger Grafiken -- auch im mathematischen Bereich -- ist heute Standard. Der Computer erlaubt darüber hinaus, durch interaktive Variation verschiedenster Parameter anschauliche Momentaufnahmen von früher nur schwer visualisierbaren Prozessen ,,in Echtzeit`` darzustellen. Es werden eine Reihe solch interaktiver Programme vorgestellt, z.B. die Kontraktion von beliebig vorgebbaren Flächen durch Oberflächen-Verringerung, Partikelsimulationen, Gleichverteilung von Punkten auf Oberflächen, Optimierung ebener und räumlicher Voronoi-Diagramme, Faltung von beweglichen Polyedern usw.

#### Mathematisches Kolloquium

**Title:**From Irrational Numbers to Perfect Matchings - 100 Years of Markov´s Uniqueness Conjecture

**Speaker:**Martin Aigner (Freie Universität Berlin)

**Date:**Freitag 18.10.2013 16:00 Kaffeepause 16:30 Vortrag

**Room:**Steyrergasse 30 Kaffeepause: C208, 2. Stock Vortrag: Hörsaal BE01, Parterre

**Abstract:**

A celebrated result in number theory is the Theorem of Markov which relates two seemingly totally different subjects: approximations of irrational numbers and the solutions of a certain equation. The proof, which Markov only sketched, was studied in great detail by Frobenius precisely 100 years ago. In his paper Frobenius mentioned a problem, now known as the uniqueness conjecture, which has remained unsolved to this day. I will tell you about the theorem and the conjecture and discuss, in particular, the amazing connections to trees, groups, combinatorics of words, lattice paths, and perfect matchings of plane graphs.

#### Gastvortrag

**Title:**Informational Divergence and Entropy on Rooted Trees with Probabilities

**Speaker:**Georg Böcherer (Technische Universität München)

**Date:**Mi 16.10.2013, 15:00 Uhr

**Room:**SR IDEG134, Inffeldgasse 16c, ground floor

**Abstract:**

Rooted trees with probabilities are used to analyze properties of a variable length code. A bound is derived on the difference between the entropy rates of the code and a memoryless source. The bound is in terms of normalized informational divergence. The bound is used to derive converses for exact random number generation, resolution coding, and distribution matching.

#### Vortrag

**Title:**Log-Ratio Analyse von Bieren, Whiskies und Kaffee's und eine praktische Anwendung an Doktoratsstudenten

**Speaker:**Matthias Templ (Vienna University of Technology, Statistics Austria)

**Date:**16.10.2013, 15.00 Uhr

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

**Abstract:**

#### Advanced Topics in Discrete Mathematics

**Title:**Automorphisms of generalised polygons

**Speaker:**Dr. James Parkinson (University of Sydney)

**Date:**Friday, 11 October 2013, 10:30 (Coffee at 10:00)

**Room:**Seminar Room 2 of the Geometry Institute, Kopernikusgasse 23/4

**Abstract:**

Abstract: Generalised polygons are certain graphs that play an important role in Lie theory. In this talk we give an introduction to this area of discrete mathematics, and discuss some recent results on automorphisms of generalised polygons. Our main aim is to provide some restrictions on how an arbitrary automorphism of a generalised polygon can act, particularly with respect to the important opposition relation in the polygon. In particular, we give a complete classification of automorphisms of finite generalised polygons which map at least one point and at least one line to an opposite, but map no chamber to an opposite chamber. One motivation for this investigation is towards the old conjectures surrounding the classification of flag-transitive finite polygons.

This is joint work with Beukje Temmermans and Hendrik Van Maldeghem.

#### Vortrag

**Title:**Fast Boundary Element Methods: Coupling with Finite Element Methods and Applications

**Speaker:**Dr. Günther Of (Institut für Numerische Mathematik, TU Graz)

**Date:**Montag, 7.10.2013, 11:15 Uhr s.t.

**Room:**Seminarraum für Statistik, Kopernikusgasse 24/3, TU Graz

**Abstract:**

The coupling of finite and boundary element methods has been attractive for the numerical solution of second order boundary value problems for decades. In particular, so-called non-symmetric formulations have been very popular in applications for a long time. But the results on the stability of related discrete systems were quite unsatisfying. In the last few years significant progress has been made in the analysis of non-symmetric formulations.

In this talk, recent results on the stability of these formulations are presented and supported by numerical examples. The use of fast boundary element methods for the coupling is demonstrated for fluid-structure interaction problems within the design of ships.

While boundary element methods are advantageous in various situations, the use of fast, data-sparse methods is a postulate for the application of boundary element methods to real world problems. In this talk, a bundle of applications of fast boundary element methods is discussed. These are adaptive boundary element methods, industrial applications in the context of electrostatics and magnetostatics, the Gauss problem, X-ray tomography, and shape optimization.

#### Vortrag

**Title:**Uniform distribution theory, almost everywhere convergence, and GCD sums

**Speaker:**Dipl.Ing. Dr. Christoph Aistleitner (TU Graz)

**Date:**Montag, 7.Oktober 2013, 10.00 Uhr s.t.

**Room:**Seminarraum f. Statistik, Kopernikusgasse 24/3, TU Graz

**Abstract:**

Abstract: The theory of uniform distribution modulo 1 is intimately

connected with the theory of trigonometric sums. In particular, results

concerning the uniform distribution modulo 1 of parametric sequences are

often proved using similar results for Fourier series or series of

dilated functions, both in the $L^2$ and in the almost everywhere sense.

In this talk, a brief account of the historical development of the

connection between uniform distribution theory, discrepancy theory,

metric number theory, Fourier analysis and probability theory is given.

It is shown how in the investigation of these problems certain sums

involving greatest common divisors arise in a natural way, and how

recent estimates for such GCD sums can be used to obtain a Carleson-type

maximal inequality for sums of dilated functions, which led to the

solution of an a.e. convergence problem which has been open for several

decades. The talk is based on joint work with Istvan Berkes and Kristian

Seip.

#### Vortrag

**Title:**Examples of 3D Self-Affine Tiles with Simple Topology

**Speaker:**Jun LUO (Sun Yat Sen University, Guangzhou, China)

**Date:**4.10.2013, 11:00

**Room:**Montanuniversität Leoben

**Abstract:**

We construct self-affine tiles of dimension $n\geq 3$ and show

that they are homeomorphic with the cube $[0,1]^n$. None of those

tiles are a self-affine polytope or the product of an $n-1$

dimensional self-affine tile with an interval. We also explain

why we are interested in such examples.

#### Mittagsseminar

**Title:**Estimating the Number of Triangulations of a Planar Point Set

**Speaker:**Raimund Seidl (Univ. Saarland)

**Date:**Friday 04.10.2013 12:15

**Room:**IST Seminarraum, Inffeldgasse 16b, 2nd floor

**Abstract:**

Like all problems in \#P, determining the number of straight edge triangulations of a planar point set admits an unbiased estimator that can be computed in polynomial expected time. I will discuss the practicability and usefulness of such estimators.

#### Mittagsseminar

**Title:**Compatible bichromatic matchings

**Speaker:**Luis Felipe Barba (Université libre de Bruxelles)

**Date:**03.10.2013 12:15

**Room:**IST Seminarraum, Inffeldgasse 16b, 2nd floor

**Abstract:**

For a set $R$ of $n$ red points and a set $B$ of $n$ blue points, a BR-matching is a non-crossing geometric perfect matching where each segment has one endpoint in $B$ and one in $R$. Two BR-matchings are compatible if their union is also non-crossing. We prove that, for any two distinct BR-matchings $M$ and $M'$, there exists a sequence of BR-matchings $M = M_1 ,\dots, M_k = M'$ such that $M_{i-1}$ is compatible with $M_i$. This implies the connectivity of the compatible bichromatic matching graph containing one node for each BR-matching and an edge joining each pair of compatible BR-matchings.

#### Seminarvortrag

**Title:**Projektive Strukturen, Traktoren und invariante Differentialoperatoren

**Speaker:**Caroline Moosmüller (Univ. Wien)

**Date:**1.10.2013, 15:00 Uhr

**Room:**Seminarraum 2, Inst. f. Geometrie, Kopernikusgasse 24

**Abstract:**

Im Rahmen einer Masterarbeit mit dem Titel ``Projective structures, tractors and invariant differential operators'' beschäftige ich mich mit Traktorbündeln und Traktorkonnexionen im Fall von projektiven Strukturen auf Mannigfaltigkeiten. Das Ziel dieser Arbeit ist es, den damit verbundenen Traktorkalkül ausführlich aufzubereiten und invariante Differentialoperatoren zu konstruieren. Desweiteren werden die Ergebnisse auf dem flachen Modell (der Sphäre) interpretiert.

#### Strukturtheorie-Seminar

**Title:**Enumeration of clique trees of chordal graphs

**Speaker:**Christoph Temmel (VU Amsterdam)

**Date:**Tuesday 1.10.2013, 11 Uhr c.t.

**Room:**A206, Steyrergasse 30, 2. Stock, Geodäsietrakt

**Abstract:**

Abstract: (joint with Florian Lehner) A chordal graph is a graph containing no induced cycle of length greater than three. A famous result by Gavril states, that a graph is chordal, iff it can be represented by a family of subtrees of a tree. The natural representations of a chordal graph are given by a subclass of the spanning trees of its clique graph, called the clique trees. We present a novel, local condition on edges of the clique graph to be a member of a clique tree. This allows us to enumerate all clique trees of a given chordal graph.

#### Miniworkshop

**Title:**Schrödinger operators with Delta-interactions on manifolds

**Speaker:**()

**Date:**24.09.2013, 10:00 - 17:00 Uhr

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

**Abstract:**

Program

10:00-11:00 I. Popov (St. Petersburg)

Laplacian perturbation supported by line and regular approximation

11:00-12:00 M. Jex (Prague)

Discrete spectrum of a strong 0-interaction supported by a planar loop

14:00-15:00 C. Kühn (Graz)

Schrödinger operators with -potentials on manifolds

15:00-16:00 M. Holzmann (Graz)

Approximate solutions for evolution equations for weighted Laplacians

16:00-17:00 V. Lotoreichik (Graz)

Schrödinger operators with - and 0-interactions on Lipschitz surfaces

and chromatic numbers of associated partitions

#### Mini-Workshop

**Title:**Phase Transitions in Random Graphs

**Speaker:**()

**Date:**Friday 20.9.2013, 08:50-16:00

**Room:**Lecture Theatre BE01, Steyrergasse 30

**Abstract:**

Plenary Speaker:

\hspace{0.5cm} Oliver Riordan (University of Oxford)

Invited Speakers:

\hspace{0.5cm} Oliver Cooley (Graz University of Technology)

\hspace{0.5cm} Charilaos Efthymiou (Goethe University Frankfurt am Main)

Further details can be found at

\hspace{0.5cm} http://www.math.tugraz.at/mathb/index.php?link=miniworkshop

**Title:**Leoben-Ljubljana Seminar on Graph Theory

**Speaker:**()

**Date:**Montag, 16.9. + Dienstag 17.9.2013

**Room:**Graz, Bildungshaus Mariatrost, Seminarraum 5

**Abstract:**

For the programme and other information, see

www.math.tugraz.at/discrete/ll13/

Daytime visitors who wish to attend some talks are kindly asked to inform the organisers via

discrete@math.tugraz.at

#### Strukturtheorie-Seminar

**Title:**Martin boundary forRandom walks with unbounded jumps on hyperbolic groups

**Speaker:**Sebastien Gouezel (Univ. Rennes I)

**Date:**Wednesday, 11.9.2013, 11 Uhr c.t.

**Room:**SR A306, Steyrergasse 30, 3. Stock, Geodäsietrakt

**Abstract:**

The identification of the Martin boundary of random walks with bounded jumps on hyperbolic groups dates back to Ancona in the 80's. It is a crucial tool to understand the properties of such random walks. We will explain how to obtain similar results for random walks with possibly unbounded jumps (under a necessary

condition of super-exponential moment). Applications to the local limit theorem will also be discussed.

#### Zahlentheoretisches Kolloquium

**Title:**INTERACTIONS BETWEEN RAMSEY THEORY AND COMBINATORICS ON WORDS

**Speaker:**Dr. Michelangelo Bucci (University of Turku, Finland)

**Date:**Montag, 19. 8. 2013, 14:00 Uhr, s.t.

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

**Abstract:**

According to Wikipedia, Ramsey Theory is a branch of mathematics that

studies conditions under which order must appear. Coherently with this

definition, one of the most common studied topics in Ramsey Theory is

formed by Partition Regular properties, that is properties of sets

(usually of nonnegative integers) that cannot be destroyed by finite

partitioning.

In this talk we will examine some interactions between Ramsey Theory and

Combinatorics on Words, observing how some key objects of Ramsey Theory

can be used to gain a new understanding on the structure of wide classes

of words and how, vice-versa, a good knowledge of the combinatorial

properties of such words can be exploited to obtain new results into the

apparently distant domain of Additive Number Theory (with N. Hindman, S. Puzyinina and L. Zamboni).

#### Zahlentheoretisches Kolloquium

**Title:**Torsion-anomalous Intersections

**Speaker:**Dr. Francesco Veneziano (Georg-August-Universität Göttingen)

**Date:**Freitag, 19.Juli 2013, 10:00 Uhr s.t.

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

**Abstract:**

Abstract:

Anomalous Intersections are a fairly recent framework introduced by

Bombieri, Masser and Zannier, which comprises and generalises a vast body

of problems and conjectures in Arithmetic Geometry.

Let $V$ be a variety contained in a group variety $G$, which is usually

taken to be an abelian variety or a torus.

When intersecting $V$ with an algebraic subgroup $B$, if the intersection

$V\cap B$ has a component of dimension strictly greater than "expected",

then such a component is said to be torsion-anomalous.

In analogy with many fundamental results in the field, there are conjectures

giving geometrical conditions for the variety $V$ to have only finitely

many (maximal) torsion-anomalous subvarieties.

The formulation of these conjectures generalises famous problems such as

the Manin-Mumford Conjecture and is related to the Mordell-Lang problem.

#### Zahlentheoretisches Kolloquium

**Title:**On the failure of Kronecker's density theorem for powers of an algebraic number

**Speaker:**Dr. Maurizio Monge (Scuola Normale Superiore di Pisa)

**Date:**Freitag, 19.Juli 2013, 11:30 Uhr

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

**Abstract:**

Abstract:

We will present a quantitative estimate on the failure of Kronecker's

density theorem for the subgroup of the torus generated by the vector

formed by m powers of an algebraic number, when m is big. We prove

that the resulting subgroup is epsilon-dense, where epsilon is related

to the Mahler measure of the algebraic number. The problem is

motivated by a problem in control theory, where we assume that only

the integral part of the behaviour is known. The estimate on the

density is proved to be best-possible up to a constant, for m big

enough; this optimality is proved by means of a result on linear

recurrences of finite length, and estimates on the determinant of

Toeplitz matrices. We formulate a conjecture on the constant

provinding the best possible estimate, relating our problem to

algebraic dynamical systems on the torus. (joint work with N. Dubbini)

#### Zahlentheoretisches Kolloquium

**Title:**On the Diophantine equation $f(x)=g(y)$

**Speaker:**Prof. Dr. Michael Zieve (University of Michigan)

**Date:**Donnerstag, 18. Juli 2013, 16:00 Uhr s.t.

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

**Abstract:**

Abstract: I will explain a recent joint result classifying all

polynomials $f(x)$ and $g(x)$ for which there is an algebraic number

field $K$ such that the image sets $f(K)$ and $g(K)$ have infinite

intersection. This involves a new approach to computing the genus of an

irreducible curve of the form $f(x)=g(y)$, as well as a novel

application of the classification of finite simple groups.

#### Vortrag im Seminar Diskrete Mathematik und Optimierung

**Title:**Connectedness, Sperner's Lemma, and combinatorial problems

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

**Date:**Dienstag 16.07.2013, 14:15

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

**Abstract:**

Let $G$ be a graph whose vertex set is partitioned into classes $V_1\cup\ldots\cup V_t$. An {\it independent transversal} in $G$ is an independent set $\{v_1,\ldots,v_t\}$ in $G$ such that $v_i\in V_i$ for each $i$. Many combinatorial problems can be formulated by asking whether a certain vertex-partitioned graph has an independent transversal, for example various colouring, hypergraph matching and covering problems. We discuss how the topological connectedness of the independence complex of $G$ can be used to show the existence of independent transversals, and hence give solutions to some of these problems.

#### Zahlentheoretisches Kolloquium

**Title:**``Approximate Counting“ mit m „Countern“

**Speaker:**Prof. Dr. Helmut Prodinger (University of Stellenbosch, South Africa)

**Date:**Montag, 8.Juli 2013, 11:00 s.t.

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

**Abstract:**

Einer Idee von Cichon folgend wird der Algorithmus im Titel analysiert.

Die eintreffenden n Daten werden zufaellig auf die m Zaehler verteilt,

und das Ergebnis ist die Summe der Einzelergebnisse. Die Analyse greift

auf alte Rechnungen ueber die Pfadlaenge digitaler Suchbaeume zurueck.

Andere Zugaenge wurden von Louchard und auch von M. Fuchs vorgeschlagen.

Die Uebereinstimmung der auftretenden Konstanten direkt zu zeigen ist

ueberraschend schwierig und benuetzt Elemente der q-Analysis.

Es wird auch ueber die „m-ifizierung“ weiterer Strukturen berichtet:

m-digitale Suchbaeume, m-binare Suchbaeume, m-PORTs. (PORT = plane

oriented recursive trees)

#### Zahlentheoretisches Kolloquium

**Title:**Central limit theorems for the number of parts in a partition

**Speaker:**Prof.Dr.Stephan Wagner (University of Stellenbosch, South Africa)

**Date:**Montag, 8.Juli 2013, 10:00 s.t.

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

**Abstract:**

We consider the length (number of parts) and the number of distinct parts in a

random partition of an integer $n$ into elements of a sequence $\Lambda$. Under

very mild technical assumptions, we determine asymptotic formulae for mean and

variance and prove a central limit theorem. The limiting distribution turns out

to be Gaussian for the number of distinct parts, while one observes three

different phases for the total number of parts. In the ``borderline'' case of

Mahler partitions (partitions into powers of 2), we observe an oscillating

behaviour. This talk is based on joint work with Hsien-Kuei Hwang and Dimbinaina

Ralaivaosaona.

#### Advanced Topics Seminar

**Title:**Random walks on (mapping class) groups

**Speaker:**Giulio Tiozzo (Harvard University)

**Date:**5.7.2013, 10:30

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

**Abstract:**

Let G be a group of isometries of a metric space X. A random walk is defined by acting on some base point by a randomly chosen group element.

Starting from the 'multiplicative ergodic theorems' of Oseledets and Furstenberg, several questions have been addressed about the asymptotic behavior of such walks, for instance whether a generic sample path escapes to the boundary of X, and if it converges to a particular direction.

We will show that, under relatively mild assumptions on the geometry of X, a typical sample path lies within sublinear distance of some geodesic. We will then apply the result to the case of the mapping class group of a surface acting on Teichmueller space, answering a question of Kaimanovich. We will also see its consequences in terms of the singularity of the harmonic measure on the boundary of X.

#### Workshop "Groups, graphs, random processes"

**Title:**Recurrence of rotor-router walks

**Speaker:**Wilfried Huss (TU Graz)

**Date:**Tuesday, 2.7.2013, 16:00-16:40

**Room:**Seminar Room of the Statistics Institute, Neue Technik/III

**Abstract:**

#### Workshop "Groups, graphs, random processes"

**Title:**Centralizers and dynamics in Thompson's group V

**Speaker:**Francesco Matucci (Univ. Paris-Sud)

**Date:**Tuesday, 2.7.2013, 13:50--14:30

**Room:**Seminar Room of the Statistics Institute, Neue Technik/III

**Abstract:**

#### Workshop "Groups, graphs, random processes"

**Title:**Combinatorial, probabilistic and analytical aspects in the theory of Automata Groups

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

**Date:**Tuesday, 2.7.2013, 11:30--12:10

**Room:**Seminar Room of the Statistics Institute, Neue Technik/III

**Abstract:**

#### Workshop "Groups, graphs, random processes"

**Title:**Rotor-router models

**Speaker:**Ecaterina Sava-Huss (TU Graz)

**Date:**Monday, 1.7.2013, 13:20--14:00

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

**Abstract:**

#### Workshop "Groups, graphs, random processes"

**Title:**Clustering in random geometric graphs on hyperbolic spaces

**Speaker:**Elisabetta Candellero (University of Birmingham)

**Date:**Monday, 1.7.2013, 11:00--11:40

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

**Abstract:**

#### Workshop "Groups, graphs, random processes"

**Title:**Groups of measurable currents and relative property (T)

**Speaker:**Markus Neuhauser (TU Aachen)

**Date:**Monday, 1.7.2013, 9:30-10:10

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

**Abstract:**

#### Advanced Topics Seminar

**Title:**An introduction to wild topology

**Speaker:**Greg Conner (Brigham Young University)

**Date:**28.6.2013, 10:15

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

**Abstract:**

We will discuss the basic tools of fundamental groups of locally complicated spaces including the study of infinite words. We will discuss some of the standard examples, such as the Hawaiian earring, and what makes them interesting. We will talk about a number of classical and recent results about these groups due to the speaker, Cannon, Eda, Kent and others.

#### Zahlentheoretisches Kolloquium

**Title:**Normal and non-normal numbers with respect to Markov partitions

**Speaker:**Manfred Madritsch (Université de Lorraine, Frankreich)

**Date:**Freitag, 28. 6. 2013, 14.15 Uhr

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

**Abstract:**

A real number in $[0,1]$ is called normal, if for any positive integer

$k$ and any block $B\in\{0,1,\ldots,q-1\}^k$ of digits of length $k$

the number of occurrences of this block within the $q$-ary expansion

is equal to the expected limiting frequency, namely $q^{-k}$. In the

first part of the talk we want to start with various equivalent

definitions of normal numbers. Then we provide constructions of normal

numbers by different methods. We will end the first part considering

normal numbers to different bases. In the second part we switch to

non-normal numbers. Constructing sets of essentially and extremely

non-normal numbers we show that these numbers are interesting from a

topological point of view. Finally in part three we focus on symbolic

dynamical systems and, in particular, on Markov partitions. The aim of

this part is to show, that one can generalize the above constructions

to a certain extend also to these numeration systems.

#### Strukturtheorie-Seminar

**Title:**Isotropic Markov semigroups on ultra-metric spaces

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

**Date:**Donnerstag, 27.6.2013, 15:00 s.t. (!!)

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

**Abstract:**

This will be a very informal and introductory talk about the recent collaboration of Bendikov, Girgor'yan, Pittet and Woess.

In the past 30 years, ultra-metric Markov processes, the associated ``Laplacians'' and their analysis have been considered by various authors, with some emphasis on the sitation where the ultrametric space is the p-adic field. The recent approach initiated by Bendikov and Grigory'an is particularly attractive because of its conceptual clarity. It leads to very complete results on recurrence/transience, transition kernel estimates and the spectrum of the Markov operator. The results are strongly linked with random walks on infinite trees.