Seminars

For the Swiss-Austrian LaWiNe seminar, see the web-site or poster. More upcoming events on the EPFL memento.

Click title for abstract

• Thursday 31 May 2012, 13:15 at MA 12
  Soyoung Moon (Dijon)
  Actions hautement transitives de produits libres

  Une action d'un groupe sur un ensemble dénombrable infini est dite hautement transitive si l'action est transitive sur l'ensemble des k-uplets d'éléments distincts pour tout nombre naturel k. Dans cet exposé, en exploitant des méthodes de la généricité au sens de Baire, on va démontrer que les produits libres admettent une action fidèle et hautement transitive si et seulement s'ils ne sont pas isomorphes au groupe diédral infini. C'est un travail en collaboration avec Yves Stalder.

• Thursday 24 May 2012, 13:15 at MA 12
  Thomas Barthelmé (Neuchâtel & Strasbourg)
  A Natural Finsler-Laplace operator

  A Finsler metric on a manifold is defined by a family of norms on each tangent spaces, hence generalizing Riemannian metrics. In this talk, we will introduce a Finsler-Laplace operator as an average of the second directional derivatives with respect to an angle measure naturally associated with the Finsler metric.
  Despite not being the first generalization of the Laplacian to Finsler metrics, we believe that the simplicity of the definition of this operator makes it more amenable to study. We will show for instance that we can control its spectrum on surface and that we can sometimes hear the non-reversibility of a Finsler drum (these results are joint work with Bruno Colbois).

• Thursday 10 May 2012, 13:15 at MA 12
  Nicolas Monod (EPFL)
  Simple amenable groups

  After reviewing briefly the notion of amenability for groups and actions, we present the first construction of simple amenable groups (infinite, f.g.). This was recently obtained in joint work with K. Juschenko.

• Thursday 10 May 2012, 10:30 at PH H3 31
  Henrik Petersen (København & EPFL)
  L²-Betti numbers for locally compact groups

  TBA

• Thursday 19 April 2012, 13:15 at MA 12
  Sabine Burgdorf (EPFL)
  Trace-positive polynomials and the tracial moment problem

  A polynomial in noncommuting variables is trace-positive if it has only nonnegative trace under all evaluations of symmetric matrices of any size. A nice certificate for trace-postivity is given by being a sum of hermitian squares and commutators. The advantage of such an algebraic certificate to test for positivity will be explained. Further, I will show similarities and differences between sums of hermitian squares and trace-positive polynomials. In the last part the "dual" point of view will be presented resulting in the tracial moment problem, a natural extension of the classical moment problem from Functional Analysis.

• Thursday 5 April 2012, 13:15 at MA 12
  Constantin Vernicos (Montpelier)
  Volume entropy and Approximability in Hilbert Geometry

  Les géométries de Hilbert sont des géométries construites à l'intérieur d'un convexe sur le modèle projectif de la géométrie hyperbolique. L'entropie volumique est un invariant associé à ces géométries qui donne une information sur la vitesse de croissance du volume des boules métriques lorsque leur rayon grandit. La conjecture en cours est qu'elle est maximal lorsque le convexe est une ellipse: celle-ci n'a été vérifié qu'en dimension deux. En reliant celle-ci à un second invariant, l'approximabilité, qui mesure la complexité à approcher un convexe par des polytopes, nous obtenons une démonstration de la conjecture en dimension 2 et 3.

• Thursday 15 March 2012, 13:15 at MA 12
  Marc Troyanov (EPFL)
  Hilbert's geometry in convex domains

  A convex domain in a vector space carries a natural complete metric introduced by Hilbert in 1895. This metric is projective, that is straight lines are geodesics. Thus Hilbert geometries are solution to Hilbert's forth problem. The Hilbert geometry in a convex domain has been the object of intense researches over the last 10 years. The goal of this lecture is to give a short introduction to Hilbert geometry and to give an overview of some recent results and open questions in the area.
  This talk is a sequel, but is independent from last week's lecture.

• Thursday 8 March 2012, 13:15 at MA 12
  Marc Troyanov (EPFL)
  On Hilbert's fourth problem

  Hilbert's fourth problem asks for a classification of all metrics on a convex sets in Euclidean space whose geodesics are the Euclidean straight lines, and for a description of the corresponding geometries. In this talk, I will give a historical perspective on the problem. I will describe the particular solution proposed by Hilbert himself and I will explain why this so-called "Hilbert geometry" is canonical. If time permits, I will also talk on some recent development on the general solution.

• Thursday 1 March 2012, 13:15 at MA 12
  Nicolas Monod (EPFL)
  The Wiegold problem

  Can you kill a perfect group with a single bullet? This question was raised by James Wiegold in the early 1970s but remains completely open to this day. I will present the solution to a variation on the same theme and indicate a relation to ring theory.

• Happy new year 2102!
• Thursday 15 December 2011, 13:15 at MA 30
  Rostyslav Kravchenko (University of Chicago)
  Self-similar groups and measures of digit tiles

  TBA

• Thursday 8 December, 13:15 at MA 30
  Anthony Arnold (EPFL)
  Large hyperbolic polygons and hyperelliptic Riemann surfaces

  A "large hyperbolic n-gon" is a set of n points P={p_1, ..., p_n} in the Poincaré disc such that there exists n non-intersecting geodesic lines l_j going respectively through p_j, each separating the disc into one "empty" half-plane and one half-plane containing all the other points (and lines).
  In this lecture, I would like to present a criterion for a polygon to be large, as well as to motivate how large hyperbolic polygons can be a useful tool in studying hyperelliptic Riemann surfaces.

• Thursday 24 November, 13:15 at MA 30
  Tsachik Gelander (Jerusalem & ETHZ)
  On the growth of Betti numbers of arithmetic groups

  We study the asymptotic behavior of the Betti numbers of higher rank locally symmetric manifolds as their volumes tend to infinity, and prove a uniform version of the Lueck Approximation Theorem, which is much stronger than the linear upper bounds proved by Gromov. The basic idea is to adapt the theory of local convergence, originally introduced for sequences of graphs of bounded degree by Benjamimi and Schramm, to sequences of Riemannian manifolds. Using rigidity theory we are able to show that when the volume tends to infinity, the manifolds locally converge to the universal cover in a sufficiently strong manner that allows one to derive the convergence of the normalized Betti numbers. Similarly, and more generally, we show that the normalized multiplicity of any unitary representation converges to its Plancherel measure. For congruence covers of a fixed manifold, we also obtain sharper estimates in terms of the rate of convergence.
  Joint work with Abert, Bergeron, Biringer, Nikolov, Raimbault, Samet.

• Thursday 17 November, 13:15 at MA 30
  Haskell Rosenthal (Austin)
  A weighted bilateral shift which is a possible counter-example to the Hyperinvariant Subspace Problem.
• Thursday 3 November, 15:00 at MA 31
  Michael Björklund (ETHZ)
  Ergodic theory and product sets in groups

  I will discuss some new approaches to the analysis of product sets in countable amenable groups via ergodic theory which have been developed in collaboration with A. Fish (Madison), and if time permits, mention a few interesting connections to some hard unsolved problems in harmonic analysis.

• Thursday 27 October, 13:15 at MA 30
  Benoît Daniel (Nancy)
  Surfaces à courbure moyenne constante dans les variétés homogènes

  Les surfaces à courbure moyenne constante (CMC) sont les surfaces qui minimisent l'aire (localement) sous une certaine contrainte de volume renfermé. Elles interviennent notamment dans le problème isopérimétrique. Un théorème de H. Hopf affirme que les seules surfaces CMC dans l'espace euclidien de dimension 3 qui sont difféomorphes à la sphère sont les sphères rondes. Nous présenterons des généralisations de ce résultat lorsque l'espace ambiant est une variété riemannienne homogène de dimension 3.

• Thursday 13 October, 13:15 at MA 30
  Gábor Elek (EPFL)
  On hyperfiniteness

  I will introduce the notion of a hyperfinite action and discuss its relation with amenable actions.

• Thursday 22 September, 13:15 at MA 30
  Monica Ilie (Lakehead)
  Fourier algebra homomorphisms and beyond

  (no abstract)