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Spring Semester 2010

Date / Time Speaker Title Location
24 February 2010
15:45-16:45 		Anke Pohl
MPIM Bonn
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Geometry Seminar

Title Maass cusp forms for Hecke triangle groups and closed geodesics
Speaker, Affiliation Anke Pohl, MPIM Bonn
Date, Time 24 February 2010, 15:45-16:45
Location HG G 43
Abstract Maass cusp forms are certain eigenfunctions of the Laplace-Beltrami operator which are of particular interest in number theory and physics. If $H$ denotes the upper half plane and $\Gamma$ is a Hecke triangle group, then the length spectrum of closed geodesics on $\Gamma\backslash H$ is generated by the Selberg zeta function. The Selberg trace formula shows that the zeros of the Selberg zeta function and the eigenvalues of Maass cusp forms are in bijection. For the Hecke triangle group $\PSL(2,\Z)$ combination of work by D. Mayer, and Lewis and Zagier provides an explicit isomorphism between Maass cusp forms and eigenfunctions of a transfer operator (evolution operator) which arises from a symbolic dynamics for the geodesic flow on $\PSL(2,\Z)\backslash H$. These eigenfunctions encode, via the Fredholm determinant of the transfer operator, the zeros of the Selberg zeta function. As a by-product, they prove the relation between zeros and eigenvalues avoiding the Selberg trace formula. I will report on work in progress joint with Martin Möller towards a uniform generalization of this so-called transfer operator method to all cofinite Hecke triangle groups.
Maass cusp forms for Hecke triangle groups and closed geodesicsread_more
HG G 43
3 March 2010
15:45-16:45 		Damian Osajda
Wroclaw
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Geometry Seminar

Title A construction of high dimensional Gromov hyperbolic Coxeter groups
Speaker, Affiliation Damian Osajda, Wroclaw
Date, Time 3 March 2010, 15:45-16:45
Location HG G 43
Abstract We provide a simple combinatorial construction of Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension. It is the simplest construction of high dimensional Gromov hyperbolic groups known to us. It is more elementary than the previous constructions of systolic Coxeter groups given by Januszkiewicz-Swiatkowski and Haglund. Moreover, we are able to construct groups that are not systolic. On the other hand various versions of the construction allows us to give new examples of systolic groups and of groups with interesting asphericity properties.
A construction of high dimensional Gromov hyperbolic Coxeter groupsread_more
HG G 43
10 March 2010
15:45-16:45 		Bruce Kleiner
NYU
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Geometry Seminar

Title A new proof of Gromov's theorem on groups of polynomial growth
Speaker, Affiliation Bruce Kleiner, NYU
Date, Time 10 March 2010, 15:45-16:45
Location HG G 43
A new proof of Gromov's theorem on groups of polynomial growth
HG G 43
17 March 2010
15:45-16:45 		Roberto Monti
Padova
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Geometry Seminar

Title Recent progress on the Heisenberg isoperimetric problem
Speaker, Affiliation Roberto Monti, Padova
Date, Time 17 March 2010, 15:45-16:45
Location HG G 43
Abstract In the setting of the Heisenberg group, we discuss the problem of minimizing a notion of left-invariant perimeter for sets under a volume constraint. The problem has a solution and the shape of the optimal set was conjectured by Pansu in the '80s. While the conjecture is still open, we shall discuss some recent progress on the problem.
Recent progress on the Heisenberg isoperimetric problemread_more
HG G 43
24 March 2010
15:45-16:45 		Roman Sauer
Münster
Details

Geometry Seminar

Title Integrable measure equivalence and rigidity of hyperbolic lattices (joint work with Uri Bader and Alex Furman)
Speaker, Affiliation Roman Sauer, Münster
Date, Time 24 March 2010, 15:45-16:45
Location HG G 43
Integrable measure equivalence and rigidity of hyperbolic lattices (joint work with Uri Bader and Alex Furman)
HG G 43
31 March 2010
15:45-16:45 		Andreas Thom
Universität Leipzig
Details

Geometry Seminar

Title Stability of unitary representations
Speaker, Affiliation Andreas Thom, Universität Leipzig
Date, Time 31 March 2010, 15:45-16:45
Location HG G 43
Abstract Long ago, Stanislaw Ulam set up a programme which studied the perturbation of algebraic identities in a metric context. In this talk, I will present results about uniform deformations and perturbations of unitary representations of discrete groups. In joint work with Narutaka Ozawa and Marc Burger, we showed for example that finite-dimensional epsilon-representation of certain lattices in semi-simple algebraic groups are epsilon-close to unitary representations. The proof relies on recent advances on bounded generation of certain lattices in semi-simple algebraic groups.
Stability of unitary representationsread_more
HG G 43
* 7 April 2010
Details

Geometry Seminar

Title Easter Break
Speaker, Affiliation
Date, Time 7 April 2010,
Location
Easter Break
14 April 2010
15:45-16:45 		Jean-Claude Picaud
Tours/FIM
Details

Geometry Seminar

Title Hopf-Sullivan Dichotomy in non positive curvature
Speaker, Affiliation Jean-Claude Picaud, Tours/FIM
Date, Time 14 April 2010, 15:45-16:45
Location HG G 43
Documents abstract_picaudfile_download
Hopf-Sullivan Dichotomy in non positive curvatureread_more
HG G 43
21 April 2010
15:45-16:45 		Alexandre Girouard
Neuchâtel
Details

Geometry Seminar

Title Geometric control of the spectrum of the Dirichlet-to-Neumann map
Speaker, Affiliation Alexandre Girouard, Neuchâtel
Date, Time 21 April 2010, 15:45-16:45
Location HG G 43
Geometric control of the spectrum of the Dirichlet-to-Neumann map
HG G 43
28 April 2010
15:45-16:45 		Masato Mimura
University of Tokyo and EPFL
Details

Geometry Seminar

Title Fixed point properties and second bounded cohomology of universal lattices on Banach spaces
Speaker, Affiliation Masato Mimura, University of Tokyo and EPFL
Date, Time 28 April 2010, 15:45-16:45
Location HG G 43
Fixed point properties and second bounded cohomology of universal lattices on Banach spaces
HG G 43
5 May 2010
15:45-16:45 		Ruth Charney
Brandeis
Details

Geometry Seminar

Title Divergence and quasimorphisms of right-angled Artin groups
Speaker, Affiliation Ruth Charney, Brandeis
Date, Time 5 May 2010, 15:45-16:45
Location HG G 43
Abstract The divergence of a geodesic $\alpha$ measures the length of the shortest path between two points on $\alpha$ that stays outside the ball of radius r about their midpoint. We give a group theoretic criterion for determining when a geodesic in a right-angled Artin group G has super-linear divergence. We use this to describe the structure of the asymptotic cone of G and to show that every subgroup of G has an infinite dimensional space of quasimorphisms. (Joint work with Jason Behrstock)
Divergence and quasimorphisms of right-angled Artin groupsread_more
HG G 43
12 May 2010
15:45-16:45 		Dr. Theo Bühler
ETH Zurich, Switzerland
Details

Geometry Seminar

Title Injective Hulls and Applications to Bounded Cohomology
Speaker, Affiliation Dr. Theo Bühler, ETH Zurich, Switzerland
Date, Time 12 May 2010, 15:45-16:45
Location HG G 43
Abstract We describe injective hulls of Banach G-modules in several ways. Among other things, this yields a new description of the canonical semi-norm in bounded cohomology.
Injective Hulls and Applications to Bounded Cohomologyread_more
HG G 43
* 19 May 2010
11:15-12:15 		Nicolas Monod
EPFL
Details

Geometry Seminar

Title Littlewood and large forests
Speaker, Affiliation Nicolas Monod, EPFL
Date, Time 19 May 2010, 11:15-12:15
Location HG G 26.1
Abstract Motivated by a classical result of Sz.-Nagy in functional analysis, Dixmier asked in 1950 which group representations can be made unitary. This question is still open, but I will report on some progress obtained with Epstein and Ozawa. We approach the question with ideas borrowed from XIXth century electricity theory as well as from contemporary percolation theory. As a result, we obtain notably non-unitarizable representations for Burnside groups and a new characterization of amenability. (The talk will be expository.)
Littlewood and large forestsread_more
HG G 26.1
26 May 2010
15:45-16:45 		Eugene Gutkin
UCLA
Details

Geometry Seminar

Title Security and insecurity
Speaker, Affiliation Eugene Gutkin, UCLA
Date, Time 26 May 2010, 15:45-16:45
Location HG G 43
Security and insecurity
HG G 43
2 June 2010
15:45-16:45 		Stefan Wenger
University of Illinois at Chicago
Details

Geometry Seminar

Title Nilpotent groups without exactly polynomial Dehn function
Speaker, Affiliation Stefan Wenger, University of Illinois at Chicago
Date, Time 2 June 2010, 15:45-16:45
Location HG G 43
Abstract The Dehn function of a finitely presented group plays an important role in geometric group theory. It is a quasi-isometry invariant and measures the complexity of the word problem for a given group. This talk is concerned with the growth of the Dehn function of nilpotent groups. For such groups many upper and a few lower bounds are known. A well-known question asks whether the Dehn function of a nilpotent group must always grow exactly like a polynomial. I will explain in this talk how recently developed methods from geometric measure theory, from the Analysis on metric spaces, and from geometric group theory can be used to give a negative answer to this question.
Nilpotent groups without exactly polynomial Dehn functionread_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: Theo Bühler, Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Enrico Le Donne, 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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