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Wintersemester 2012/2013

Oberseminar: Geometry and Analysis

Gerasim Kokarev and Jan Swoboda
(Mathematisches Institut der LMU)

Time and venue:
Donnerstag 14 Uhr c.t. Hörsaal B134 des Mathematischen Instituts. Ab 13.45 Uhr Tee im 3. Stock.

18 October 2012
kein Vortrag

25 October 2012
R. Schmidt (LMU München) Non-leaves with small coarse homology groups.
Abstract. We present a construction of Riemannian manifolds that cannot be quasi-isometric to leaves in a codimension one foliation of a compact manifold. Starting from an arbitrary non-compact Riemannian manifold, we deform the metric in such a way that the resulting Riemannian manifold is not quasi-isometric to a leaf, while the coarse homology groups remain unchanged. In particular, this construction yields non-leaves whose coarse homology groups are that of the Euclidean space.

1 November 2012

8 November 2012
A. Hassannezhad (Neuchatel) Eigenvalue estimates in the light of Weyl's law.
Abstract. Eigenvalues of the Laplacian are Riemannian invariants. There is a deep relation between these eigenvalues and other geometric invariants. We study geometric upper bounds on the eigenvalues which are consistent with their asymptotic behavior known as the Weyl Law.

15 November 2012
kein Vortrag

22 November 2012
F. Fillastre (Cergy) Reversed Alexandrov-Fenchel inequalities.
Abstract. We consider the Minkowski addition and the volume of closed convex sets, invariant under the action of a given cocompact lattice of SO(d,1). Their support functions are defined on compact hyperbolic manifolds rather than on the sphere. In the regular and the polyhedral cases, Alexandrov--Fenchel inequalities are derived. Here the inequalities are reversed and the proofs, although very similar to the original ones by A.D. Alexandrov, are simpler than for the classical case of convex bodies. arXiv:1112.5353

29 November 2012
F. Witt (WWU Münster) Higgs bundles and the Hausel conjecture.

6 December 2012
B. Springborn (TU München) Combinatorial Ricci flow on triangulated surfaces.
Abstract. I will review Feng Luo's "Combinatorial Yamabe flow on surfaces" (in two dimensions, Ricci flow is the same as Yamabe flow) and show how one can avoid the problem of degenerating triangles to obtain a flow that is defined for all positive times and converges. This is based on the connection with three-dimensional hyperbolic polyhedra that was developed in a paper with A. Bobenko and U. Pinkall.

13 December 2012
I. Izmestiev (FU Berlin) A variational proof of the infinitesimal rigidity of smooth convex surfaces.
Abstract. A classical theorem due to Liebmann and Blaschke states that every compact smooth surface in R^3 with positive Gauss curvature is infinitesimally rigid. We give a new proof of this theorem based on the variations of the Hilbert-Einstein functional (half the total scalar curvature plus twice the total mean curvature of the boundary) on a class of warped product metrics. This approach is related to the Koiso theorem on rigidity of Einstein manifolds with curvature constraints. Also it is in a sense dual to a proof of rigidity in the Minkowski problem that uses the variations of the volume.

20 December 2012
M. Amann (KIT Karlsruhe) Cohomological consequences of (almost) free group actions.
Abstract. PDF

10 January 2013
kein Vortrag

17 January 2013
kein Vortrag

24 January 2013
E. Cabezas-Rivas (WWU Münster) A generalization of Gromov's almost flat manifold theorem.
Abstract. Taking as a starting point a question by John Lott about the vanishing of the $\hat A$-genus for spin almost non-negatively curved manifolds, we conjecture that an almost non-negatively curved manifold is either conformally equivalent to a manifold with positive scalar curvature or it is finitely covered by a Nilmanifold. In the way to prove such a claim, we found a generalization of Gromov's almost flat manifold theorem where $L^\infty$-bounds for the curvature are relaxed to mixed curvature bounds. During the talk, we will give the precise statement of our theorem and a detailed sketch of the proof. This is a joint work with Burkhard Wilking.

31 January 2013
A. Pohl (Göttingen) Entropy and escape of mass for discrete geodesic flows in rank one situations.
Abstract. It is well-known that on compact spaces, metric entropy is upper semi-continuous and mass cannot escape. On non-compact spaces the situation changes drastically. Given any homogeneous space of the form L\G, where G is any connected semisimple Lie group of real rank one with finite center and L is a non-cocompact lattice in G, we will discuss a relationship between the metric entropy of homogeneous diagonal flows on L\G and escape of mass. This is joint work with Manfred Einsiedler and Shirali Kadyrov.

Last modified: 3 Jan 2013