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Autumn Semester 2011

Date / Time Speaker Title Location
21 September 2011
15:45-16:45 		Egor Shelukhin
Tel Aviv, Israel
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Geometry Seminar

Title Constructing quasimorphisms via moment maps
Speaker, Affiliation Egor Shelukhin, Tel Aviv, Israel
Date, Time 21 September 2011, 15:45-16:45
Location HG G 43
Abstract We describe a construction of a quasimorphism on the universal cover of a group that acts on a contractible symplectic space with an equivariant moment map, and with an equivariant system of 'geodesic' paths - whenever the areas of 'geodesic' triangles have uniformly bounded symplectic areas. Applications include a non-trivial quasimorphism on the universal cover of the Hamiltonian group of every symplectic manifold of finite volume (reinterpreting, in particular, the quasimorphisms of Ruelle, Barge-Ghys, Entov and Py) and a reinterpretation of the Guichardet-Wigner quasimorphisms in the finite dimensional case of Hermitian Lie groups.
Constructing quasimorphisms via moment mapsread_more
HG G 43
28 September 2011
15:45-16:45 		Nicolas Monod
EPFL, Switzerland
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Geometry Seminar

Title Fixed points and derivations
Speaker, Affiliation Nicolas Monod, EPFL, Switzerland
Date, Time 28 September 2011, 15:45-16:45
Location HG G 43
Abstract We overview some relations between fixed point theorems and derivations of Banach algebras. We prove a new fixed point theorem for L^1 spaces and their non-commutative analogues and examine their consequences for derivation problems. The approach is completely geometric. Joint work with Bader and Gelander.
Fixed points and derivationsread_more
HG G 43
5 October 2011
15:45-16:45 		Gábor Elek
Alfréd Rényi Institute of Mathematics, Hungary, and EPFL, Switzerland
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Geometry Seminar

Title Quasi-invariant means and Zimmer amenability
Speaker, Affiliation Gábor Elek, Alfréd Rényi Institute of Mathematics, Hungary, and EPFL, Switzerland
Date, Time 5 October 2011, 15:45-16:45
Location HG G 43
Abstract Let G be a discrete group acting on itself with left multiplication. We give a necessary and sufficient condition for the action to have a quasi-invariant mean with a given cocycle. This is the combinatorial version of the characterization of Benjamin Miller for the Borel case. Then we show a geometric condition that guarantees that the corresponding action on the Cech-Stone compactification is Zimmer amenable. The geometric condition (weighted hyperfiniteness) resembles Property A. We do not know the exact relation between the two notions. However, we can show that amenable groups and groups of finite asymptotic dimension are weighted hyperfinite. (Joint work with Adam Timar)
Quasi-invariant means and Zimmer amenabilityread_more
HG G 43
19 October 2011
15:45-16:45 		Igor Rivin
Temple University, USA
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Geometry Seminar

Title Asymptotic phenomena in geometric group theory
Speaker, Affiliation Igor Rivin, Temple University, USA
Date, Time 19 October 2011, 15:45-16:45
Location HG G 43
Abstract I will discuss properties of generic elements and generic finitely generated subgroups in (generic?) geometrically interesting groups (lattices in semi-simple lie groups, mapping class groups, (outer) automorphism groups of free groups.
Asymptotic phenomena in geometric group theoryread_more
HG G 43
2 November 2011
15:45-16:45 		David Ralston
Ben Gurion University, Israel
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Geometry Seminar

Title Ergodicity of Natural Staircases
Speaker, Affiliation David Ralston, Ben Gurion University, Israel
Date, Time 2 November 2011, 15:45-16:45
Location HG G 43
Abstract Without assuming much background on translation surfaces, we will define square-tiled surfaces and "natural staircases" over them (a certain construction of a Z^d periodic cover). In joint work with S. Troubetzkoy (Luminy), we will show that subject to certain natural, explicit, and easily checkable conditions, geodesic flow on such infinite surfaces is ergodic in almost every direction.
Ergodicity of Natural Staircasesread_more
HG G 43
9 November 2011
15:45-16:45 		Jouni Parkkonen
University of Jyvaskyla, Finland
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Geometry Seminar

Title Counting common perpendiculars in negative curvature
Speaker, Affiliation Jouni Parkkonen, University of Jyvaskyla, Finland
Date, Time 9 November 2011, 15:45-16:45
Location HG G 43
Abstract Let N(t) be the number of locally geodesic common perpendicular arcs of length at most t between two nonempty convex subsets of a finite volume hyperbolic manifold. The asymptotic behaviour of N(t) is known for arcs between two points (Huber, Margulis) and between a point and a totally geodesic submanifold (Herrmann, Eskin-McMullen) etc. I will discuss my recent work with F. Paulin on extending these results.
Counting common perpendiculars in negative curvatureread_more
HG G 43
* 21 November 2011
14:00-15:00 		Vitaly Bergelson
Ohio State University, USA
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Geometry Seminar

Title Uniform distribution, generalized polynomials and dynamical systems
Speaker, Affiliation Vitaly Bergelson, Ohio State University, USA
Date, Time 21 November 2011, 14:00-15:00
Location HG G 19.1
Abstract A classical theorem due to H. Weyl states that if P is a polynomial over R such that at least one of its coefficients (other than the constant term) is irrational, then the sequence P(n), n=1,2,... is uniformly distributed mod 1. We will discuss some recent extensions of this theorem which involve "generalized polynomials", that is, functions which are obtained from the conventional polynomials by the use of the greatest integer function, addition and multiplication. We will explain the role of dynamical systems in obtaining these results and discuss some of the connections with and applications to the theory of Diophantine approximations and combinatorics of Ramsey theory.
Uniform distribution, generalized polynomials and dynamical systemsread_more
HG G 19.1
23 November 2011
15:45-16:45 		Joachim Hilgert
University of Paderborn, Germany
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Geometry Seminar

Title Patterson-Sullivan distributions in higher rank
Speaker, Affiliation Joachim Hilgert, University of Paderborn, Germany
Date, Time 23 November 2011, 15:45-16:45
Location HG G 43
Abstract For a compact locally symmetric space of non-positive curvature and arbitrary rank, we consider sequences of normalized joint eigenfunctions which belong to the principal spectrum of the algebra of invariant differential operators. Using a semiclassical pseudodifferential calculus, we define and study lifted quantum limits as weak*-limit points of Wigner distributions. The Helgason boundary values of the eigenfunctions allow us to construct Patterson-Sullivan distributions on the space of Weyl chambers. These distributions are asymptotic to lifted quantum limits and satisfy additional invariance properties, which makes them useful in the context of quantum ergodicity. Our results generalize results for compact hyperbolic surfaces obtained by Anantharaman and Zelditch.
Patterson-Sullivan distributions in higher rankread_more
HG G 43
30 November 2011
15:45-16:45 		Klaus Schmidt
University of Vienna and ESI, Austria
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Geometry Seminar

Title Mahler measure, Fuglede-Kadison determinants and entropy of algebraic actions
Speaker, Affiliation Klaus Schmidt, University of Vienna and ESI, Austria
Date, Time 30 November 2011, 15:45-16:45
Location HG G 43
Abstract If $\Gamma$ is a countable discrete group one can associate with every $f$ in the integer group ring $Z\Gamma$ a $\Gamma$-action $\alpha_f$ by continuous automorphisms of a compact abelian group $X_f$. This talk is about elementary dynamical properties of such actions. In particular I will discuss the entropy of such an action $\alpha_f$, which in the case of $\Gamma =Z^d$ is given by the logarithmic Mahler measure of $f$. If $\Gamma$ is amenable, the entropy of $\alpha_f$ coincides with the logarithm of the Fuglede-Kadison determinant of $f$, viewed as an element of the group-von Neumann algebra of $\Gamma$. The latter result was proved under various additional assumptions in recent years by Deninger, Deninger-Schmidt, and Hanfeng Li, with a very recent complete solution by Hanfeng Li and Andreas Thom.
Mahler measure, Fuglede-Kadison determinants and entropy of algebraic actionsread_more
HG G 43
7 December 2011
15:45-16:45 		Tsachik Gelander
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Israel
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Geometry Seminar

Title Representations of F_n and actions of Aut(F_n)
Speaker, Affiliation Tsachik Gelander, Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Israel
Date, Time 7 December 2011, 15:45-16:45
Location HG G 43
Representations of F_n and actions of Aut(F_n)
HG G 43
14 December 2011
15:45-16:45 		Anke Pohl
ETH Zürich, Switzerland
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Geometry Seminar

Title Period functions for Maass cusp forms via symbolic dynamics
Speaker, Affiliation Anke Pohl, ETH Zürich, Switzerland
Date, Time 14 December 2011, 15:45-16:45
Location HG G 43
Abstract Maass cusp forms are non-holomorphic eigenfunctions of the Laplace-Beltrami operator which are invariant under the action of a given lattice in PSL(2,R) and which decay rapidly towards any cusp. They were discovered in number theory in 1949 and soon seen to be essential for various fields, in particular, harmonic analysis, representation theory and physics. Despite intensive research, to date in general for a non-uniform lattice, no single Maass cusp form is explicitely known. For some lattices, Maass cusp forms have been shown to be linear isomorphic to so-called period functions. These are highly regular functions on (parts of) the real axis which satisfy a certain functional equation depending on the lattice. I will report on work in progress dedicated to deduce functional equations and definitions of period functions (for a wide class of non-uniform lattices) using symbolic dynamics for the geodesic flow.
Period functions for Maass cusp forms via symbolic dynamics read_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: Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Anke Pohl, 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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