Departement Mathematik

Geometry seminar

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Frühjahrssemester 2015

Datum / Zeit Referent:in Titel Ort
18. Februar 2015
15:45-16:45 		Vadim Kaimanovich
University of Ottawa
Details

Geometry Seminar

Titel Boundary actions of random subgroups (joint with Jan Cannizzo)
Referent:in, Affiliation Vadim Kaimanovich , University of Ottawa
Datum, Zeit 18. Februar 2015, 15:45-16:45
Ort HG G 43
Abstract One of the most basic questions one can ask about a general measure class preserving action of a countable group is that about its conservativity vs. dissipativity (i.e., absence or presence of non-trivial wandering sets). If one looks at the action of a subgroup on the boundary of an ambient group, then for general subgroups this action may well be conservative, dissipative or mixed, whereas the action of normal subgroups is usually conservative. I will show that the boundary actions of random subgroups on the Poisson boundary of an ambient group is always conservative provided the distribution of these subgroups is stationary (in particular, invariant). The proof uses rigidity properties of the Radon-Nikodym cocycle of Poisson boundary bundles and their equivariant quotients. As a corollary this result implies conservativity of the action of random subgroups of a finitely generated free group on the geometric boundary endowed with the uniform measure. I will also discuss related problems for fundamental groups of negatively curved manifolds.
Boundary actions of random subgroups (joint with Jan Cannizzo)read_more
HG G 43
25. Februar 2015
15:45-16:45 		Barak Weiss
Tel Aviv University
Details

Geometry Seminar

Titel The illumination problem and the SL(2,R) action on the moduli space of translation surfaces, following Eskin-Mirzakhani-Mohammadi
Referent:in, Affiliation Barak Weiss, Tel Aviv University
Datum, Zeit 25. Februar 2015, 15:45-16:45
Ort HG G 43
The illumination problem and the SL(2,R) action on the moduli space of translation surfaces, following Eskin-Mirzakhani-Mohammadi
HG G 43
4. März 2015
15:45-16:45 		Anders Karlsson
Université de Genève
Details

Geometry Seminar

Titel Metric spaces, their functionals and spectral results
Referent:in, Affiliation Anders Karlsson, Université de Genève
Datum, Zeit 4. März 2015, 15:45-16:45
Ort HG G 43
Abstract I will discuss how horofunctions, or metric functionals, play a common role in results of spectral or ergodic type, such as mean ergodic theorems, multiplicative ergodic theorems, Thurston's spectral theorem for surface homeomorphisms, Wolff-Denjoy results for holomorphic maps. In particular, I plan to mention recent on-going work joint with S. Gouëzel.
Metric spaces, their functionals and spectral results read_more
HG G 43
11. März 2015
15:45-16:45 		Sunio Yamada
Gakushuin University
Details

Geometry Seminar

Titel Convex geometry on Teichmueller space
Referent:in, Affiliation Sunio Yamada, Gakushuin University
Datum, Zeit 11. März 2015, 15:45-16:45
Ort HG G 43
Abstract I will talk about how the language of convex geometry is effective in describing the shape of the Teichmueller space of a closed surface from several viewpoints. An emphasis is on the Weil-Petersson geometry, yet we will compare it to the geometry of the Teichmueller metric, as well as that of the Thurston asymmetric metric.
Convex geometry on Teichmueller spaceread_more
HG G 43
1. April 2015
15:45-16:45 		Wilderich Tuschmann
Universität Karlsruhe
Details

Geometry Seminar

Titel Rigidity and Stability in Positive Scalar Curvature
Referent:in, Affiliation Wilderich Tuschmann, Universität Karlsruhe
Datum, Zeit 1. April 2015, 15:45-16:45
Ort HG G 43
Abstract I will discuss several new stability and classification results for Riemannian and, in particular, Einstein manifolds with positive scalar curvature, yielding isometry or diffeomorphism to spherical space forms. This is joint work with M. Wiemeler from Augsburg.
Rigidity and Stability in Positive Scalar Curvatureread_more
HG G 43
15. April 2015
15:45-16:45 		Jouni Parkkonen
University of Jyväskylä, Finland
Details

Geometry Seminar

Titel C-Fuchsian subgroups of Picard modular groups
Referent:in, Affiliation Jouni Parkkonen, University of Jyväskylä, Finland
Datum, Zeit 15. April 2015, 15:45-16:45
Ort HG G 43
Abstract A C-Fuchsian subgroups of Picard modular groups stabilizes a complex geodesic line in the projective model of the complex hyperbolic plane. I will describe the commensurability classes of maximal C-Fuchsian groups and I will discuss the behaviour of the orbits under the Picard modular groups of the complex geodesics and their boundaries at infinity (called chains) which are ellipses or lines in the Heisenberg group. The talk is based on joint work with F. Paulin.
C-Fuchsian subgroups of Picard modular groupsread_more
HG G 43
29. April 2015
15:45-16:45 		Athanase Papadopoulos
Université de Strasbourg
Details

Geometry Seminar

Titel On the arc metric on Teichmüller space
Referent:in, Affiliation Athanase Papadopoulos, Université de Strasbourg
Datum, Zeit 29. April 2015, 15:45-16:45
Ort HG G 43
On the arc metric on Teichmüller space
HG G 43
6. Mai 2015
15:45-16:45 		Enrico Leuzinger
TU Karlsruhe
Details

Geometry Seminar

Titel Higher-dimensional filling functions for some CAT(0) spaces and applications to S-arithmetic groups
Referent:in, Affiliation Enrico Leuzinger, TU Karlsruhe
Datum, Zeit 6. Mai 2015, 15:45-16:45
Ort HG G 43
Abstract Let X=S x B be the product of a symmetric space S of noncompact type with a product B of Euclidean buildings. Let L be a discrete group acting isometrically and cocompactly on X. We describe a familiy of quasi-isometry invariants for such L, namely the k-dimensional Dehn functions, which measure the difficulty to fill k-spheres by (k+1)-balls. Since L is quasi-isometric to X, assertions about Dehn-functions for L follow from corresponding results for filling functions for X. Basic examples of groups L as above are uniform S-arithmetic subgroups of semisimple groups defined over global fields. I will also discuss a (mostly) conjectural picture for non-uniform S-arithmetic groups.
Higher-dimensional filling functions for some CAT(0) spaces and applications to S-arithmetic groupsread_more
HG G 43
13. Mai 2015
15:45-16:45 		Michael Dymond
Universität Innsbruck
Details

Geometry Seminar

Titel Sets containing a point of differentiability of every Lipschitz function
Referent:in, Affiliation Michael Dymond, Universität Innsbruck
Datum, Zeit 13. Mai 2015, 15:45-16:45
Ort HG G 43
Abstract Sets containing a point of differentiability of every Lipschitz function have been the focus of much modern interest. In this talk we discuss the existence of exceptional universal differentiability sets and present some striking structural properties that they exhibit. We also point out possible directions of future research in this area. The research presented in this talk formed part of my PhD thesis, supervised by Olga Maleva.
Sets containing a point of differentiability of every Lipschitz functionread_more
HG G 43
20. Mai 2015
15:45-16:45 		Clara Löh
Universität Regensburg
Details

Geometry Seminar

Titel Manifolds with small integral simplicial volume
Referent:in, Affiliation Clara Löh, Universität Regensburg
Datum, Zeit 20. Mai 2015, 15:45-16:45
Ort HG G 43
Abstract Integral simplicial volume is the minimal weighted number of simplices needed to represent an integral fundamental cycle of a given manifold. On the one hand, integral simplicial volume lacks most of the convenient inheritance properties of Gromov's original real simplicial volume, and hence is rather difficult to compute. On the other hand, a better understanding of integral simplicial volume could lead to a better understanding of the relation between real simplicial volume and the Euler characteristic. In this talk, we will characterise manifolds with integral simplicial volume equal to 1 and derive an elementary non-computability statement for integral simplicial volume.
Manifolds with small integral simplicial volumeread_more
HG G 43
27. Mai 2015
15:45-16:45 		Robert Young
University of Toronto
Details

Geometry Seminar

Titel Filling multiples of embedded curves
Referent:in, Affiliation Robert Young, University of Toronto
Datum, Zeit 27. Mai 2015, 15:45-16:45
Ort HG G 43
Abstract Filling a curve with an oriented surface can sometimes be "cheaper by the dozen". For example, L. C. Young constructed a smooth curve drawn on a projective plane in R^n which is only about 1.5 times as hard to fill twice as it is to fill once and asked whether this ratio can be bounded below. We will use methods from geometric measure theory to answer this question and pose some open questions about systolic inequalities for surfaces embedded in R^n.
Filling multiples of embedded curvesread_more
HG G 43
17. Juni 2015
15:45-16:45 		Polixeny Spilioti
Details

Geometry Seminar

Titel Ruelle and Selberg zeta functions on compact hyperbolic odd-dimensional manifolds
Referent:in, Affiliation Polixeny Spilioti,
Datum, Zeit 17. Juni 2015, 15:45-16:45
Ort HG G 43
Abstract In this talk, we will present some recent work on the zeta functions of Ruelle and Selberg on compact hyperbolic manifolds X of odd dimension d. These are dynamical zeta functions associated with the geodesic flow on the unite sphere bundle S(X) . We define the Selberg zeta function $Z(s; \sigma, \chi)$ and the Ruelle zeta function $R(s; \sigma, \chi)$ in terms of finite dimensional representation $\sigma$ and $\chi$ and prove that they converge in some half-plane Re(s) > c . We prove also that they admit a meromorphic continuation to the whole complex plane and describe the singularities of the Selberg zeta function in terms of the discrete spectrum of certain twisted differential operators on X. The main tool that we use is the Selberg trace formula for integral trace class operators induced by the flat Laplacian $\Delta^\#$, acting on smooth sections of a twisted vector bundle, first introduced by Müller. We generalize results of Bunke and Olbrich to the case of non-unitary representations $\chi$ of the fundamental group of $X$.
Ruelle and Selberg zeta functions on compact hyperbolic odd-dimensional manifoldsread_more
HG G 43

Organisatoren:innen: Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Viktor Schröder

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09 FS 09

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