Talks and events

Rudolf Riedi (EIA Fribourg): Characteristic functions and diverging moments

Using a wavelet analysis we relate the regularity of the characteristic function to the tail of its distribution function and, thus, to the existence of moments. Exploiting properties of the Fourier transform we derive a simple non-parametric estimator of the tail index. A background in basic analysis is sufficient to follow the arguments. If time permits we demonstrate the accuracy of the estimator in comparison with classical tail estimators.

Thomas Mountford (EPFL): Contact Processes on Trees

We consider a growth model called the contact process in various environments and show that such a process on a tree of bounded degree must survive for an exponential (in the number of vertices) amount of time provided the parameter of infection is above a natural critical value.

Tan Ser Peow (National University of Singapore): Length series identities on hyperbolic surfaces

We will discuss various length series identities on hyperbolic surfaces and their applications due to Basmajian, McShane, Mirzakhani, Bridgeman and various other authors. In particular, we will present a unified approach for obtaining these identities and we will also discuss how this can be used to derive a new identity for closed hyperbolic surfaces involving the dilogarithm of the lengths of simple closed geodesics, in recent joint work with Feng Luo.

Emanuele Delucchi (Bremen): Toric arrangements

A toric arrangement is given by a family A of level sets of characters of a complex torus T. The study of these objects is a fairly recent topic at the crossroads of combinatorics, topology and algebra.
The focus of this talk will be on the topology of the complement M:=T \ A, and in particular on the extent to which it is determined by the combinatorial data of the arrangement A.
After an introduction to toric arrangements and a review of known results, I will present some recent joint work with Giacomo d'Antonio, focusing on the fundamental group of M and on the proof that M is a minimal space (and thus homologically torsion-free).

Kevin Wildrick (Universität Bern): Koebe's Kreisnormierungsproblem in metric spaces

In 1908, Koebe conjectured that every domain in the two-dimensional sphere is conformally equivalent to a circle domain, i.e., a domain whose complementary components are points or round disks. Koebe himself confirmed this conjecture for finitely connected domains, but it was not until 1993 that He and Schramm confirmed the conjecture in the countably connected case. The full conjecture remains open. We will discuss a version of this problem for metric spaces that are homeomorphic to a domain in the plane. In this setting, which is inspired by geometric group theory and rigidity theory, there is no a priori smooth structure with which to define the notion of conformality. Instead, we employ a similar condition, called quasisymmetry, which is assumed to hold at all scales and has a rich family of intuitive geometric invariants.

Cédric Villani (Lyon): Des triangles, des gaz et des hommes

Pascal J. Thomas (Toulouse): Fonctions de Green pluricomplexes

La fonction de Green classique est liée à la solution du problème de Dirichlet pour les fonctions harmoniques (solution fondamentale du Laplacien), et peut être vue comme une enveloppe supérieur de fonctions sousharmoniques. L'étude des fonctions holomorphes de plusieurs variables complexes mène à considérer des fonctions plurisousharmoniques, qui sont sousharmoniques le long de chaque direction complexe, et la fonction de Green pluricomplexe peut être définie comme enveloppe supérieure de fonctions plurisousharmoniques. Son maniement est plus délicat, car l'opérateur dont elle est une "solution fondamentale" n'est pas linéaire. On donnera quelques unes de ses relations avec des problèmes extrémaux naturels (ou qui nous plaisent), notamment avec le comportement des fonctions holomorphes bornés dans un domaine donné qui s'annulent sur un ensemble fini de points de donnés ; et quelques exemples de comportement asymptotique quand ces points se confondent.

Michel Benaïm (Neuchâtel): Jeux, Dynamique et Apprentissage

Gerhard Rosenberger (Hamburg): On the surface group conjecture and embeddings of surface groups into one-relator groups

Let $F$ be a finitely generated free group, $\bar{F}$ an isomorphic copy of $F$, $W$ a word in $F$ and $\bar{W}$ its copy in $\bar{F}$. A Baumslag double is a free product of $F$ and $\bar{F}$ amalgamated via $\bar{W}=W$. For example, an orientable surface group of genus 2 is a Baumslag double, and it is known that a Baumslag double is a hyperbolic group if and only if $W$ is not a proper power of in F. We will discuss what conditions make fundamental groups of orientable and nonorientable surfaces of finite genus embed into Baumslag doubles, and also present recent results concerning the Surface Group Conjecture, which states: Suppose that G is a non-free, non-solvable one-relator group such that every subgroup of finite index is again a one-relator group and every subgroup of infinite index is a free group. Then G is a surface group.

Christopher Judge (Indiana): The music of triangles

Imagine a thick triangular sheet of metal vibrating so much that it produces a resonant tone. Are there are two qualitatively different types of vibrational behavior that lead to the same tone? The answer is yes for both the equilateral triangle and the right isoceles triangle. In joint work with Luc Hillairet (Nantes), we show that the answer is `no' for the generic triangle without explicitly identifying a single triangle for which the answer is no. In this talk, I will describe the underlying mathematics and the new method---asymptotic separation of variables--- which solves this and similar problems.

Robert Young (Toronto): Quantifying simple connectivity: an introduction to the Dehn function

Many theorems start by taking an existence theorem and asking "How many?" or "How big?" or "How fast". The best-known example may be the prime number theorem. Euclid proved that infinitely many primes exist, and the prime number theorem describes how quickly they grow. I'll discuss what happens when you apply the same idea to simple connectivity. In a simply-connected space, any closed curve is the boundary of some disc, but how big is that disc? And what can that tell you about the geometry of the space?

Will Cavendish (Princeton) : Finite-sheeted covers of 3-manifolds and the Cohomology of Solenoids

Pierre Dehornoy (Berne) : Flot géodésique, sections de Birkhoff et enlacement

Muriel Heistercamp (Neuchâtel): Counting closed Reeb-orbits in spherizations

Martin Herrmann(Fribourg/KIT): Minimal Models

Alexey Muranov (Toulouse): Stable commutator length and conjugation-invariant normes in infinite simple groups

Nicolas Weisskopf: Rational Homotopy Theory: An Introduction to Sullivan Algebras

Lev Kiwi (UniFr): $\mathbb{Q}$-homotopy theory - Part III

The aim of this talk is to present the homotopy theory of CDGA's.

Anand Dessai: Formal spaces

Bruno Duchesne (Hebrew University): Espaces symétriques riemanniens de dimension infinie

Gerald Gotsbacher (Tata): Aritmetic groups and Hodge theory

In this talk, I shall describe a Hodge-theoretic problem in the cohomology of arithmetic groups and our attempt to solve it. In order to convey ideas rather than machinery, I will take most of the time to illustrate the situation in the case of arithmetic quotients of real hyperbolic 2-space. To be more specific, suppose $G$ be a linear reductive algebraic group of Hermitian type defined over $\mathbb{Q}$, and $\Gamma$ an arithmetic subgroup of $G$ acting on the associated Hermitian symmetric domain $X$. Moreover, let $\mathbb{V}$ be a homogeneous local system on the orbit space $M$ and denote by $M^\ast$ the Satake--Baily--Borel compactification of $M$. The intersection cohomology $IH^\bullet(M^\ast,\mathbb{V})$ carries a (pure) Hodge structure of weight equal degree, and our problem is to construct -- functorially in $\mathbb{V}$ -- a complex of coherent sheaves on $M^\ast$ that resolves $\mathbb{V}$ and the hypercohomology of which computes this Hodge structure. In case $G=GL(2)$, the task reduces to a Hodge-theoretic reinterpretation of the Eichler--Shimura isomorphism.

Alexander Lytchak (Muenster)

Martin Herrmann: Rational ellipticity

Jérôme Scherer (EPFL): Conjugation spaces and manifolds

After a short introduction to Hausmann, Holm, and Puppe's theory of conjugation spaces and manifolds, I want to show how one can use this structure to construct equivariant Chern classes for Real bundles (in the sense of Atiyah). The second part of the talk will be devoted to realization problems, known examples and open questions in low dimension.

Pascal Rolli (ETHZ) : Constructing Quasimorphisms

Fribourg Weekend in Group Theory

Program and registration here.

Gergana Bencheva (Bulgarian Academy of Sciences): Computer Modelling and Simulation of Haematopoietic Stem Cells Migration

The therapy of various pathological blood diseases consists mainly of two steps - a chemotherapy and a whole body irradiation to eradicate the patient's haematopoietic system is followed by a transplantation of haematopoietic stem cells (HSCs), obtained from the mobilized peripheral blood of a donor. After transplantation, HSCs find their way to the stem cell niche in the bone marrow. Upon homing HSCs have to multiplicate rapidly to regenerate the blood system. Adequate computer models for these steps would help medical doctors to shorten the period in which the patient is missing their effective immune system. Our attention is focused on the numerical solution of a mathematical model for the chemotactic movement of HSCs, which consists of a nonlinear system of chemotaxis equations coupled with an ordinary differential equation on the boundary of the domain in the presence of nonlinear boundary conditions. Theoretical and practical issues related to the numerical approximation of the model and especially to the nonlinear boundary conditions will be discussed in the talk.

Michel Matter (Genève): Modèle des tas de sable et graphes autosimilaires

Jeroen Schillewaert (Université libre de Bruxelles): The geometries of the Freudenthal-Tits magic square

Claude Marion (Einstein Institute Jerusalem): Triangle generation of finite simple groups and rigidity

Michele D'Adderio (Universität Göttingen): Geometric theory of algebras

Riemannian Topology Meeting

The RTM aims to bring together PhD students and Post-Docs from different universities, and to give them the opportunity to share new ideas and results in the areas of geometry and topology. The meeting is intended for mathematicians interested in the interplay of algebraic topology and Riemannian geometry.

For more information, please visit our website:

math.unifr.ch/riemannian_topology

Brent Everitt (York)