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Herbstsemester 2012

Datum / Zeit Referent:in Titel Ort
10. Oktober 2012
15:45-16:45 		Alexander Gorodnik
University of Bristol
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Geometry Seminar

Titel Zn-actions on nilmanifolds
Referent:in, Affiliation Alexander Gorodnik, University of Bristol
Datum, Zeit 10. Oktober 2012, 15:45-16:45
Ort HG G 43
Abstract We discuss mixing properties of commuting automorphisms of nilmanifolds and establish a quantitative estimate on decay of correlations which has applications to probabilistic limit theorems, cohomological equations and rigidity. This is a joint work with Spatzier.
Zn-actions on nilmanifoldsread_more
HG G 43
17. Oktober 2012
15:45-16:45 		Richard Schwartz
Brown University/Oxford University
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Geometry Seminar

Titel Polytope exchange transformations, lattices, and renormalization
Referent:in, Affiliation Richard Schwartz, Brown University/Oxford University
Datum, Zeit 17. Oktober 2012, 15:45-16:45
Ort HG G 43
Abstract Polytope exchange transformations are higher dimensional analogues of interval exchange transformations, the latter being closely related to subjects such as billiards and Teichmuller theory. I will explain some natural constructions of polytope exchange transformations based on Euclidean lattices, and I will describe my results concerning the simplest nontrivial example, which is a 1-parameter family of polygon exchange transformations. I will explain how hyperbolic lattices arise as a group of "renormalization symmetries" of the 1-parameter family.
Polytope exchange transformations, lattices, and renormalizationread_more
HG G 43
* 24. Oktober 2012
16:05-17:05 		David Cimasoni
Université de Genève
Details

Geometry Seminar

Titel The critical temperature for the Ising model on planar graphs
Referent:in, Affiliation David Cimasoni, Université de Genève
Datum, Zeit 24. Oktober 2012, 16:05-17:05
Ort HG G 43
Abstract The Ising model is one of the simplest models to exhibit a "phase transition", that is, a sharp change of behavior when some parameter (here, the temperature) crosses some critical value. In this talk, I will explain how to determine the critical temperature of the Ising model on any biperiodic planar weighted graph (or equivalently, on any finite weighted graph embedded in the torus). Although this result lies in the realm of statistical physics, the statement is formulated in homological terms, and the proof uses several geometric tools (Kramers-Wannier duality on surfaces, Harnack curves,…) This is joint work with Hugo Duminil-Copin.
The critical temperature for the Ising model on planar graphsread_more
HG G 43
31. Oktober 2012
15:45-16:45 		Goulnara Arzhantseva
Universität Wien
Details

Geometry Seminar

Titel Analytic properties of infinitely presented groups
Referent:in, Affiliation Goulnara Arzhantseva, Universität Wien
Datum, Zeit 31. Oktober 2012, 15:45-16:45
Ort HG G 43
Abstract We provide new examples of finitely generated infinitely presented groups satisfying (various) Baum-Connes conjectures. These are among certain infinitely presented small cancellation groups. The talk is based on joint works with Cornelia Drutu (on the Rapid Decay property of such groups) and with Damian Osajda (on the Haagerup property of those groups).
Analytic properties of infinitely presented groupsread_more
HG G 43
7. November 2012
15:45-16:45 		Yair Hartman
Weizman Institute, Israel
Details

Geometry Seminar

Titel The Furstenberg entropy realization problem
Referent:in, Affiliation Yair Hartman, Weizman Institute, Israel
Datum, Zeit 7. November 2012, 15:45-16:45
Ort HG G 43
Abstract Given a group equipped with a measure, one may consider all its stationary actions and their corresponding entropy values. The "Furstenberg entropy realization problem" is to describe this set of possible values. Although stationary actions always exist, there are very few known examples of such. Recently, L. Bowen introduced a new way of constructing stationary spaces given an IRS (a probability measure on the space of subgroups of G, which is invariant under conjugations). We will use IRS's on the lampligher group to realize interesting entropy values for lamplighers over amenable groups and free groups with large class of measures. This is a joint work with Omer Tamuz.
The Furstenberg entropy realization problemread_more
HG G 43
14. November 2012
15:45-16:45 		Corinna Ulcigrai
University of Bristol
Details

Geometry Seminar

Titel Ergodic properties of some periodic billiards and infinite translation surfaces
Referent:in, Affiliation Corinna Ulcigrai, University of Bristol
Datum, Zeit 14. November 2012, 15:45-16:45
Ort HG G 43
Abstract In a mathematical billiard a particle moves without friction in a planar domain bouncing elastically at the boundary. In this talk we consider a class of infinite periodic billiards, which includes the billiard in a strip with periodically spaced barriers and the wind-tree model, introduced in 1912 by Ehrenfest, which is a planar billiard consisting of rectangular scatterers placed on the integer grid. While the dynamical properties of billiards in bounded rational polygons is now well understood and is connected to the study of compact translation surfaces and Teichmueller dynamics, these infinite billiards can be reduced to infinite periodic translation surfaces. Basic questions such as ergodicity in this context are still poorly understood. In joint work with K. Fraczek, we show that for the above mentioned billiards, for almost every value of the parameters the billiard flow in almost every direction is not ergodic.
Ergodic properties of some periodic billiards and infinite translation surfacesread_more
HG G 43
21. November 2012
15:45-16:45 		John G. Radcliffe
Vanderbilt University
Details

Geometry Seminar

Titel On volumes of hyperbolic Coxeter polytopes and quadratic forms
Referent:in, Affiliation John G. Radcliffe, Vanderbilt University
Datum, Zeit 21. November 2012, 15:45-16:45
Ort HG G 43
Abstract In this talk, the computation of the covolume of the group of units of the quadratic form x12+x22+...+xn2-xn+12 with d an odd, square-free, positive integer, will be described. The covolume will be expressed in terms of Bernoulli numbers, Dirichlet L-functions, and powers of pi. John Mcleod has recently determined the hyperbolic Coxeter fundamental domain of the reflection subgroup of the group of units for the case d = 3. We apply our covolume formula to determine the volumes of Mcleod’s hyperbolic Coxeter polytopes.
On volumes of hyperbolic Coxeter polytopes and quadratic formsread_more
HG G 43
5. Dezember 2012
15:45-16:45 		Leonid Polterovich
Tel Aviv University
Details

Geometry Seminar

Titel Small talk on geometry of contactomorphism groups
Referent:in, Affiliation Leonid Polterovich, Tel Aviv University
Datum, Zeit 5. Dezember 2012, 15:45-16:45
Ort HG G 43
Abstract Does the universal cover of the contactomorphism group of a contact manifold admit an unbounded conjugation-invariant norm? I'll discuss a construction and an obstruction. (Joint work with Maia Fraser and Daniel Rosen.)
Small talk on geometry of contactomorphism groupsread_more
HG G 43
12. Dezember 2012
15:45-16:45 		Pablo Suárez-Serrato
UNAM, Mexico
Details

Geometry Seminar

Titel On the minimal volume of higher graph manifolds
Referent:in, Affiliation Pablo Suárez-Serrato, UNAM, Mexico
Datum, Zeit 12. Dezember 2012, 15:45-16:45
Ort HG G 43
Abstract We will show vanishing and positivity results of certain asymptotic invariant for a family manifolds inspired on 3-dimensional graph manifolds. Bounds for the minimal volume entropy will be given, in terms of the volume of locally symmetric pieces. This is all joint work with C. Connell, and answers questions raised by Frigerio-Lafont-Sisto.
On the minimal volume of higher graph manifoldsread_more
HG G 43

Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen.

Organisatoren:innen: Michael Björklund, Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Viktor Schröder

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