Speakers

Alberto Abbondandolo (Bochum)

Title: Some sharp systolic bounds in geometry and dynamics

Abstract: In classical systolic geometry one is interested in bounding the length of shortest closed geodesics on a Riemannian manifold in terms of the volume. I will discuss such sharp bounds for spheres of revolution. I will also discuss possible extensions of these questions to Hamiltonian dynamics.

Pierre-Emmanuel Caprace (Louvain-la-Neuve)

Title: Bounding the covolume of lattices in products

Abstract: The Kazhdan-Margulis theorem ensures that, in a semisimple Lie group without compact factors, the set of covolumes of all lattices is bounded away from 0. The goal of this talk, based on joint work with Adrien Le Boudec, is to discuss the validity of that theorem, and some of its relatives, in the broader context of lattices in products of compactly generated simple locally compact groups.

Stéphanie Cupit-Foutou (Bochum)

Title: Kählerizable multiplicity-free Hamiltonian compact manifolds

Abstract: My talk deals with multiplicity-free Hamiltonian compact manifolds acted on by a compact group, a generalization of symplectic toric manifolds. I will explain how to characterize among such manifolds those which are Kählerizable, by means of their momentum polytope. This is a joint work with G. Pezzini and B. Van Steirteghem.

Peter Heinzner (Bochum)

Title: Invariant convex sets in polar representations and geometric properties of the momentum map

Abstract: We will discuss compact invariant convex set E in polar representation of a compact Lie group K. Polar representations are given by the adjoint action of K on p, where K is a maximal compact subgroup of a real semisimple Lie group G with Lie algebra g = k ⊕ p. If a ⊂ p is a maximal subalgebra, then P = E ∩ a is a convex set in a. We show that up to conjugation the face structure of E is completely determined by that of P and that a face of E is exposed if and only if the corresponding face of P is exposed. We give a relation of these results to the geometry of actions of real forms of complex reductive groups.

Linus Kramer (Münster)

Title: Abstract homomorphisms between certain topological groups

Abstract:

We will discuss results and counterexamples concerning automatic continuity of abstract group homomorphisms between locally compact groups and discrete groups. This is joint work with O. Braun, K.H. Hofmann and O. Varghese.

Bernhard Krötz (Paderborn)

Title: Plancherel theory for real spherical spaces

Abstract: We put the Plancherel theory of Harish-Chandra, one of the most fundamental developments of 20th century mathematics, into the much wider context of real spherical spaces.

Marco Mazzucchelli (Lyon)

Title: Min-Max characterizations of Zoll Riemannian manifolds

Abstract: A closed Riemannian manifold is called Zoll when its unit-speed geodesics are all periodic with the same minimal period. This class of manifolds has been thoroughly studied since the seminal work of Zoll, Bott, Samelson, Berger, and many other authors. It is conjectured that, on certain closed manifolds, a Riemannian metric is Zoll if and only if its unit-speed periodic geodesics all have the same minimal period. In this talk, I will first discuss the proof of this conjecture for the 2-sphere, which builds on the work of Lusternik and Schnirelmann. I will then show an analogous result for certain higher dimensional closed manifolds, including spheres, complex and quaternionic projective spaces: a Riemannian manifold is Zoll if and only if two suitable min-max values in a free loop space coincide. This is based on joint work with Stefan Suhr.

Dietmar Salamon (Zürich)

Title: Complex structures, moment maps, and the Ricci form

Abstract: The talk exhibits the Ricci form as a moment map for the action of the group of exact volume preserving diffeomorphisms on the space of almost complex structures. This observation yields a new approach to the Weil—Petersson symplectic form on the Teichmüller space of isotopy classes of complex structures with real first Chern class zero and nonempty Kähler cone. As a corollary one obtains a proof of the Donaldson—Fujiki—Quillen theorem, which asserts that the scalar curvature is a moment map for the action of the group of Hamiltonian symplectomorphisms on the space of almost complex structures that are compatible with the symplectic form. This is joint work with Oscar Garcia-Prada and Samuel Trautwein.

Petra Schwer (Magdeburg)

Title: Kostant Convexity in the affine flag variety and affine grassmannian

Abstract: In this talk I will explain the classical Kostant convexity theorem and will show how one can obtain natural analogs for the affine flag variety and affine grassmannian using combinatorial and geometric methods.

Alain Valette (Neuchâtel)

Title: The space of closed subgroups of a locally compact group

Abstract: Endowed with the Chabauty topology, the space Sub(G) of closed subgroups of a locally compact group G becomes a compact space with a canonical action of G. The study of Sub(G) was revived those last years. On the one hand because of the interest for invariant random subgroups, i.e. G-invariant probability measures on Sub(G). On the other hand Sub(G) provides natural compactifications of some homogeneous spaces of G. We will illustrate this with G=SL_n(Q_p) and study the Chabauty compactification of the space of Cartan subgroups of G. (The latter is joint work with C. Ciobotaru and A. Leitner)