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Autumn Semester 2016

Date / Time Speaker Title Location
21 September 2016
15:45-16:45 		Cagri Sert
Université Paris-Sud
Event Details

Geometry Seminar

Title Asymptotics in real linear semisimple Lie groups: joint spectrum and large deviation principles
Speaker, Affiliation Cagri Sert, Université Paris-Sud
Date, Time 21 September 2016, 15:45-16:45
Location HG G 43
Abstract Let S be a bounded subset of G, (set of real points of) a connected semisimple linear real algebraic group. We are interested in understanding the asymptotics in G of the sequence of powers of S. We analyse this sequence through the classical Cartan and Jordan decompositions of G. Using these, to S, we associate a set in a Weyl chamber of G, that describes the asymptotic behaviour of elements of powers of S. We call this set the joint spectrum of S. We show that if S generates a Zariski dense semigroup in G, the joint spectrum of S is a convex body (compact convex set of non-empty interior) in the Cartan subalgebra. This immediately extends previous work of Benoist on limit cones of Zariski dense semigroups. If time permits, we mention two applications of joint spectrum to two different works of the author: first one is related to exponential growth of a finite S, and the second one, to large deviation principles for random products of elements of S. We shall give more details for the second application
Asymptotics in real linear semisimple Lie groups: joint spectrum and large deviation principlesread_more
HG G 43
12 October 2016
15:45-16:45 		Maxime Gheysens
EPF Lausanne
Event Details

Geometry Seminar

Title Hilbert spaces can affinely spot amenability
Speaker, Affiliation Maxime Gheysens, EPF Lausanne
Date, Time 12 October 2016, 15:45-16:45
Location HG G 43
Abstract Day proved in the early sixties a nice geometric fixed-point property characterising amenability via actions on locally convex spaces. We show that such a characterisation already holds in the Hilbert world. This seemingly innocuous result will be a pretext to introduce a variant of the induction of representations that allows, to some extent, to induce representations from a group when it can be considered as a "measure-theoretical subgroup" of another group. This applies notably to non-amenable groups, which contain free groups in this measure-theoretical sense thanks to a result of Gaboriau and Lyons. Joint work with Nicolas Monod.
Hilbert spaces can affinely spot amenabilityread_more
HG G 43
16 November 2016
15:45-16:45 		Sven Raum
EPF Lausanne
Event Details

Geometry Seminar

Title On the type I conjecture for groups acting on trees
Speaker, Affiliation Sven Raum, EPF Lausanne
Date, Time 16 November 2016, 15:45-16:45
Location HG G 43
Abstract A locally compact group is of type I -- roughly speaking -- if all its unitary representations can be uniquely written as a direct integral of irreducible representations. This property is of utter importance in the study of Lie groups and algebraic groups. The type I conjecture predicts that every closed subgroup of the automorphism group of a locally finite tree that acts transitively on the boundary of the tree is of type I. A proof of this conjecture would give a new perspective on the representation theory of rank one algebraic groups over non-Archimedean fields and provide a huge class of groups whose representation theory is well-behaved. I will describe my recent effort to attack the type I conjecture by operator algebraic means.
On the type I conjecture for groups acting on treesread_more
HG G 43
23 November 2016
15:45-16:45 		Gabriele Link
Karlsruhe Institute of Technology
Event Details

Geometry Seminar

Title Ergodic geometry of Hadamard spaces with a rank one isometry
Speaker, Affiliation Gabriele Link, Karlsruhe Institute of Technology
Date, Time 23 November 2016, 15:45-16:45
Location HG G 43
Abstract It has been observed a long time ago that in quotients of the hyperbolic plane by Fuchsian groups there are precisely two mutually exclusive possibilities for the behaviour of the geodesic flow: Either it is conservative and ergodic, or it is dissipative and non-ergodic (with respect to an appropriate invariant measure on the unit tangent bundle). In this talk I will explain how this so-called Hopf dichotomy can be extended to quotients of a locally compact Hadamard space $X$ by a non-elementary discrete isometry group $\Gamma$ containing a rank one isometry. Moreover, the statements in the dichotomy will be discussed and related to properties of the limit set of $\Gamma$ and to the behaviour of the Poincare series at the critical exponent. One major difference and difficulty compared to the classical case (where the geodesic flow is Anosov) consists in the possible presence of numerous flat subspaces of $X$; I will also explain how these subspaces can be sufficiently well controlled.
Ergodic geometry of Hadamard spaces with a rank one isometryread_more
HG G 43
30 November 2016
15:45-16:45 		Masato Mimura
EPF Lausanne
Event Details

Geometry Seminar

Title Superintrinsic synthesis in fixed point properties
Speaker, Affiliation Masato Mimura, EPF Lausanne
Date, Time 30 November 2016, 15:45-16:45
Location HG G 43
Abstract For a class X of metric spaces, we say a finitely generated group G has the fixed point property (F_X), relative to X, if all isometric G-actions on every member in X have global fixed points. Fix a class X of "non-positively curved spaces" (for instance, in the sense of Busemann) stable under certain operations. We obtain new criteria to "synthesize" the "partial" (F_X) (more precisely, with respect to subgroups) into the "whole" (F_X). A basic example of such X is the class of all Hilbert spaces, and then (F_X) is equivalent to the celebrated property (T) of Kazhdan (the Delorme--Guichardet theorem). Our "synthesis" is intrinsic, in the sense that our criteria do not depend on the choices of X. The point here is, nevertheless, we exclude all of "Bounded Generation" axioms, which were the clue in previous inventive works by Shalom (Publ. IHES, 1999 and ICM 2006). This settles a natural question for 15 years arising from Shalom's pioneering work that asks whether this sort of (intrinsic) synthesis is achievable. As applications, we present a rather simpler proof of (T) for elementary groups over non-commutative rings (originally proved by Ershov--Jaikin, Invent. Math., 2010). Moreover, our synthesis enables us to extend that to one in general L_p space settings for all finite p>1.
Superintrinsic synthesis in fixed point propertiesread_more
HG G 43
7 December 2016
15:45-16:45 		Nicolas Radu
UC Louvain
Event Details

Geometry Seminar

Title Simple groups acting on trees
Speaker, Affiliation Nicolas Radu, UC Louvain
Date, Time 7 December 2016, 15:45-16:45
Location HG G 43
Abstract Algebraic groups over local fields, as PSL(n,K), provide many examples of non-discrete compactly generated locally compact groups that are (topologically) simple. Let us denote by S the set of all topological groups with these properties. Groups acting on trees provide another main source of examples of groups in S: for a fixed locally finite semiregular tree T, there are infinitely many (pairwise non-isomorphic) closed subgroups of Aut(T) which belong to S. The set of closed subgroups of Aut(T) carries a natural compact topology (called the Chabauty topology), so a natural question arises: Which groups appear as Chabauty limits of simple subgroups of Aut(T)? Can we obtain new examples of groups in S by observing accumulation points of (infinitely many) well-known examples? The talk will discuss those questions as well as related topics.
Simple groups acting on treesread_more
HG G 43
14 December 2016
15:45-16:45 		Dr. Dominik Gruber
ETH Zurich, Switzerland
Event Details

Geometry Seminar

Title Small cancellation theory over Burnside groups
Speaker, Affiliation Dr. Dominik Gruber, ETH Zurich, Switzerland
Date, Time 14 December 2016, 15:45-16:45
Location HG G 43
Abstract I will discuss how combinatorics and geometry work together to provide a new and easy-to-apply tool for constructing infinite bounded torsion groups with prescribed properties. The main tools are acylindrical actions of (classical or graphical) small cancellation groups on Gromov hyperbolic spaces and the theory of periodic quotients of groups admitting such actions. As applications, we obtain Gromov monsters with bounded torsion, we show the unsolvability of numerous decision problems in categories of bounded torsion groups, and we obtain a Rips construction for bounded torsion groups. This is joint work with Rémi Coulon.
Small cancellation theory over Burnside groupsread_more
HG G 43

Organizers: Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Viktor Schröder, Alessandro Sisto

Archive: 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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