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Autumn Semester 2010

Date / Time Speaker Title Location
29 September 2010
15:45-16:45 		Talia Fernós
The Hebrew University of Jerusalem
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Geometry Seminar

Title Reduced 1-cohomology and relative property (T)
Speaker, Affiliation Talia Fernós, The Hebrew University of Jerusalem
Date, Time 29 September 2010, 15:45-16:45
Location HG G 43
Abstract The celebrated theorems of Delorme (1977) and Guichardet (1972) establish the equivalence between property (T) and the vanishing of 1-cohomology, where the coefficients are taken in a unitary representation. In 2000 Shalom proved that the (apriori) weaker condition of the vanishing of reduced 1-cohomology is in fact equivalent to property (T) for the class of compactly generated groups. In 2005-2006 de Cornulier, Jolissaint, and Fernos independently showed that the vanishing of the restriction map on 1-cohomology is equivalent to relative property (T). One may ask if the relative version of Shalom's theorem is true. In a joint work with Valette we exhibit a large class of non-compact amenable group-pairs where the restriction map on reduced 1-cohomology always vanishes. Since amenable groups can not have relative property (T) with respect to non-compact subgroups, our result gives a strong negative answer to the above question.
Reduced 1-cohomology and relative property (T)read_more
HG G 43
* 8 October 2010
11:15-12:15 		Swiatoslaw Gal
Uniwersytet Wroclawski, Poland
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Geometry Seminar

Title Extending the Kähler cocycle to the whole group of symplectic dyfeomorphisms
Speaker, Affiliation Swiatoslaw Gal, Uniwersytet Wroclawski, Poland
Date, Time 8 October 2010, 11:15-12:15
Location HG G 19.1
Abstract The Kähler cocycle is a two-cocycle classically defined on the group of isometries of a Hermitian symmetric space. We will give a definition that makes sense for the whole group of symplectic dyfeomorphisms of a symplectic manifold M with exact symplectic form and b_1(M)=0. We will discuss non-triviality of that cocycle. As an application we will give a simple proof of a theorem by Leonid Polterovich that if a discrete finitely generated group \Gamma acts on a symplectic manifold (with mild assumptions) by Hamiltonian dyfeomorphisms then the translation length of all non-trivial elements of \Gamma is non-zero. This is a joint work with Jarek Kędra from Aberdeen.
Extending the Kähler cocycle to the whole group of symplectic dyfeomorphismsread_more
HG G 19.1
13 October 2010
15:45-16:45 		Ben Warhurst
Universität Bern / Università di Milano-Bicocca
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Geometry Seminar

Title Symmetry and conformality in Sub-Riemannian geometry
Speaker, Affiliation Ben Warhurst, Universität Bern / Università di Milano-Bicocca
Date, Time 13 October 2010, 15:45-16:45
Location HG G 43
Abstract Subriemannian geometries are manifolds with a "horizontal bundle" equipped with an inner product. The horizontal bundle is a bracket generating sub-bundle of the tangent bundle which implies that the manifold is connected by horizontal paths, that is curves whose tangents lie in the horizontal bundle. The subriemannian distance is the infimum of lengths of all horizontal curves where the length is the integral of the lengths of the tangents measured by the inner product. Symmetries such as isometries or conformal maps must necessarily be contact maps, ie diffeomorphisms which preserve the horizontal bundle, and typically form finite dimensional Lie groups. The prototypical models of subriemannian geometries are called Carnot groups, ie the underlying manifold is a simply connected stratified nilpotent Lie group. The rigidity problem for Carnot groups is to classify those which have finite dimensional families of symmetries versus those which have infinite dimensional families of symmetries. In this talk I will discuss a complete solution to the rigidity problem in the class of C^2 mappings as well as a Liouville type theorem on conformal maps.
Symmetry and conformality in Sub-Riemannian geometryread_more
HG G 43
20 October 2010
15:45-16:45 		Prof. Dr. Emmanuel Kowalski
ETH Zurich, Switzerland
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Geometry Seminar

Title The sieve, in expansion
Speaker, Affiliation Prof. Dr. Emmanuel Kowalski, ETH Zurich, Switzerland
Date, Time 20 October 2010, 15:45-16:45
Location HG G 43
Abstract Recently, sieve methods have been introduced in the study of problems concerning arithmetic objects appearing in actions of discrete groups with exponential growth (for instance, in orbits of such groups on affine spaces). In such contexts, it turns out that the sieve can be applied provided a natural family of graphs related to quotients of the relevant group forms an expander family. Recent works of (among others) Kantorovich-Oh, Helfgott, Bourgain-Gamburd-Sarnak, Breuillard-Green-Tao, Pyber-Szabó, Varju, Gorodnik-Nevo, have considerably extended the range of situations where the expansion property is known. Particularly striking are those cases related to subgroups of infinite index in arithmetic groups which are Zariski-dense in the associated algebraic group. We will explain the general principles of sieve in these contexts, and discuss some of the most interesting and elegant applications, as well as some open problems.
The sieve, in expansionread_more
HG G 43
27 October 2010
15:45-16:45 		Prof. Dr. Marc Burger
ETH Zurich, Switzerland
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Geometry Seminar

Title Fundamental groups of compact Kaehler manifolds and geometric group theory
Speaker, Affiliation Prof. Dr. Marc Burger, ETH Zurich, Switzerland
Date, Time 27 October 2010, 15:45-16:45
Location HG G 43
Abstract The general topic of the talk concerns the problem of which are the additional restrictions imposed on a finitely presented group if one assumes that it is the fundamental group of a compact kaehler manifold (kaehler group). Since Gromov's seminal work showing that such a group cannot be a nontrivial free product, methods of geometric group theory have become important in that field. As an illustration, we will explain Delzant's recent result that a solvable kaehler group contains a finite index nilpotent subgroup.
Fundamental groups of compact Kaehler manifolds and geometric group theoryread_more
HG G 43
* 4 November 2010
15:45-16:45 		Giuseppe Tinaglia
King's College London
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Geometry Seminar

Title The geometry of constant mean curvature surfaces embedded in R^3
Speaker, Affiliation Giuseppe Tinaglia, King's College London
Date, Time 4 November 2010, 15:45-16:45
Location HG E 41
Abstract In this talk I will discuss recent results on the geometry of constant mean curvature (H\neq 0) surfaces embedded in R^3. Among other things I will prove a radius and curvature estimates for simply connected, constant mean curvature surfaces embedded in R^3. It follows from the radius estimate that the only complete constant mean curvature disk embedded in R^3 is the round sphere. This is joint work with Bill Meeks.
The geometry of constant mean curvature surfaces embedded in R^3read_more
HG E 41
10 November 2010
15:45-16:45
Details

Geometry Seminar

Title No talk because of conference in ETH
Speaker, Affiliation
Date, Time 10 November 2010, 15:45-16:45
Location HG G 43
No talk because of conference in ETH
HG G 43
17 November 2010
15:45-16:45 		Anders Karlsson
Université de Genève
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Geometry Seminar

Title Heat kernels and counting in Cayley graphs
Speaker, Affiliation Anders Karlsson, Université de Genève
Date, Time 17 November 2010, 15:45-16:45
Location HG G 43
Abstract We find that heat kernels of finitely generated groups are built up from terms whose main factors are Bessel functions. These explicit expressions allow for analyses of counting functions, such as the number of spanning trees or closed geodesics. Interesting constants appear in the asymptotics of counting functions in certain families of graphs: L^2 determinants, Mahler measures, determinants of Laplacians, automorphic forms, etc. Joint work with G. Chinta and J. Jorgenson.
Heat kernels and counting in Cayley graphs read_more
HG G 43
24 November 2010
15:45-16:45 		Masato Mimura
University of Tokyo
Details

Geometry Seminar

Title On quasi-homomorphisms and commutators in SL_n(A) (A: ring)
Speaker, Affiliation Masato Mimura, University of Tokyo
Date, Time 24 November 2010, 15:45-16:45
Location HG G 43
Abstract A map from a (possibly uncountable) discrete group to the set of reals is called a quasi-homomorphism if it is a homomorphism up to uniformly bounded error. This concept has natural relation to bounded cohomology, and thanks to celebrated work of Bavard, it also connects to the conception of the stable commutator length (written as SCL) on the commutator subgroup. In this talk, by studying these concepts for special linear groups over certain rings, we will provide a natural example of groups with the following interesting features: having infinite commutator width, but the SCL vanishing identically. This answers a question of Abert and Monod (ICM 2006, etc.) for the size n being sufficiently large.
On quasi-homomorphisms and commutators in SL_n(A) (A: ring)read_more
HG G 43
1 December 2010
15:45-16:45 		Emmanuel Breuillard
Université Paris-Sud 11 (Orsay)
Details

Geometry Seminar

Title Jordan's theorem on finite linear groups and its approximate analogues
Speaker, Affiliation Emmanuel Breuillard, Université Paris-Sud 11 (Orsay)
Date, Time 1 December 2010, 15:45-16:45
Location HG G 43
Abstract I will discuss two well-known proofs of Jordan's classical theorem on finite subgroups of $\GL_n(\C)$, which asserts that they contain an abelian normal subgroup whose index is bounded by a function of $n$ only. One algebraic, the other geometric. I will then describe an approximate version of the geometric proof, which yields a classification of approximate subgroups of compact Lie groups, via a Besicovitch type lemma valid in non-negative curvature. Joint work with Ben Green.
Jordan's theorem on finite linear groups and its approximate analoguesread_more
HG G 43
8 December 2010
15:45-16:45 		Koji Fujiwara
Tohoku University
Details

Geometry Seminar

Title Group actions on quasi-trees and its application
Speaker, Affiliation Koji Fujiwara, Tohoku University
Date, Time 8 December 2010, 15:45-16:45
Location HG G 43
Abstract Quasi trees are, by definition, graphs which are quasi-isometric to simplicial trees. In this talk we show mapping class groups, hyperbolic groups etc act on quasi-trees with unbounded orbits. We also discuss applications if such action exists.
Group actions on quasi-trees and its applicationread_more
HG G 43
15 December 2010
15:45-16:45 		Marshall Williams
University of Illinois at Chicago
Details

Geometry Seminar

Title Metric currents, differentiable structures, and Carnot groups
Speaker, Affiliation Marshall Williams, University of Illinois at Chicago
Date, Time 15 December 2010, 15:45-16:45
Location HG G 43
Abstract In order to formulate and solve area minimization problems in Euclidean space, Federer and Fleming introduced normal and integral currents. A far-reaching generalization of this theory was developed by Ambrosio-Kirchheim, who extended most of Federer and Fleming's results to arbitrary metric spaces. In Euclidean spaces, ``metric currents'' are the same as classical currents, provided one only considers currents of locally finite mass, and locally finite boundary mass. In more exotic metric spaces, the situation is more complicated, but there are still some similarities to the classical theory. I will some results characterizing metric currents in a large class of metric spaces, namely, those admitting generalizations of Rademachers' theorem, as formulated by Cheeger and Keith. I will particularly emphasize the special case where the underlying space is a Carnot group equipped with its Carnot-Carath\'eodory metric.
Metric currents, differentiable structures, and Carnot groupsread_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, 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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