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Autumn Semester 2012

Date / Time Speaker Title Location
10 October 2012
15:45-16:45 		Alexander Gorodnik
University of Bristol
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Geometry Seminar

Title Zn-actions on nilmanifolds
Speaker, Affiliation Alexander Gorodnik, University of Bristol
Date, Time 10 October 2012, 15:45-16:45
Location 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 October 2012
15:45-16:45 		Richard Schwartz
Brown University/Oxford University
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Geometry Seminar

Title Polytope exchange transformations, lattices, and renormalization
Speaker, Affiliation Richard Schwartz, Brown University/Oxford University
Date, Time 17 October 2012, 15:45-16:45
Location 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 October 2012
16:05-17:05 		David Cimasoni
Université de Genève
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Geometry Seminar

Title The critical temperature for the Ising model on planar graphs
Speaker, Affiliation David Cimasoni, Université de Genève
Date, Time 24 October 2012, 16:05-17:05
Location 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 October 2012
15:45-16:45 		Goulnara Arzhantseva
Universität Wien
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Geometry Seminar

Title Analytic properties of infinitely presented groups
Speaker, Affiliation Goulnara Arzhantseva, Universität Wien
Date, Time 31 October 2012, 15:45-16:45
Location 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
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Geometry Seminar

Title The Furstenberg entropy realization problem
Speaker, Affiliation Yair Hartman, Weizman Institute, Israel
Date, Time 7 November 2012, 15:45-16:45
Location 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
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Geometry Seminar

Title Ergodic properties of some periodic billiards and infinite translation surfaces
Speaker, Affiliation Corinna Ulcigrai, University of Bristol
Date, Time 14 November 2012, 15:45-16:45
Location 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
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Geometry Seminar

Title On volumes of hyperbolic Coxeter polytopes and quadratic forms
Speaker, Affiliation John G. Radcliffe, Vanderbilt University
Date, Time 21 November 2012, 15:45-16:45
Location 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 December 2012
15:45-16:45 		Leonid Polterovich
Tel Aviv University
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Geometry Seminar

Title Small talk on geometry of contactomorphism groups
Speaker, Affiliation Leonid Polterovich, Tel Aviv University
Date, Time 5 December 2012, 15:45-16:45
Location 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 December 2012
15:45-16:45 		Pablo Suárez-Serrato
UNAM, Mexico
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Geometry Seminar

Title On the minimal volume of higher graph manifolds
Speaker, Affiliation Pablo Suárez-Serrato, UNAM, Mexico
Date, Time 12 December 2012, 15:45-16:45
Location 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

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

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

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

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