| 22-feb-2012 (wed) |
Jens Marklof
|
Eigenfunctions of polygonal billiards
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15:45-16:45 |
HG G 43 |
| Abstract: |
Despite their simple geometry, billiards in polygons give rise to a rich variety of dynamical phenomena. One example is the asymptotic distribution of closed billiard trajectories, which is still only partially understood. In the present lecture I will discuss a different natural problem: the distribution of eigenfunctions of the Dirichlet Laplacian of a polygon---is the L^2 mass of the eigenfunctions highly localized or equidistributed on the billiard domain? The lecture is based on joint work with Zeev Rudnick (Tel Aviv). |
| Speakers: |
Prof. Dr. Jens Marklof
(University of Bristol, UK)
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|
| 29-feb-2012 (wed) |
Urs Lang
|
Injective hulls of metric spaces: old and new
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15:45-16:45 |
HG G 43 |
| Abstract: |
Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. In the 1960es, Isbell showed that every metric space X has an injective hull E(X) (in the category of metric spaces and 1-Lipschitz maps). After reviewing Isbell's explicit construction and some later work by Dress and others, I will discuss some recent results on injective hulls of certain discrete metric spaces and groups. If X is the vertex set of a connected locally finite graph with a uniform stability property of intervals, then E(X) is a locally finite polyhedral complex with finitely many isometry types of n-cells, isometric to polytopes in l^n_\infty, for each n. This applies to a class of finitely generated groups G, including word hyperbolic and abelian groups, among others. Then G acts properly on E(G) by cellular isometries, and the first barycentric subdivision of E(G) is a model for the classifying space \underbar{E}G for proper actions. If G is word hyperbolic, E(G) is finite dimensional and the action is cocompact; the injective hull thus provides an alternative to the Rips complex, with some extra features.
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| Speakers: |
Prof. Dr. Urs Lang
(ETH Zürich, Switzerland)
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|
| 7-mar-2012 (wed) |
Pierre Py
|
An equivariant deformation of the hyperbolic space
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15:45-16:45 |
HG G 43 |
| Abstract: |
I will explain how to construct a continuous family of ''exotic'' locally compact CAT(−1) spaces with cocompact isometry groups all isomorphic to the isometry group of the real hyperbolic space H^n. This is joint work with Nicolas Monod. |
| Speakers: |
Prof. Dr. Pierre Py
(Université de Strasbourg, France)
|
|
| 14-mar-2012 (wed) |
Frédéric Paulin
|
Equilibrium states in negative curvature
|
15:45-16:45 |
HG G 43 |
| Abstract: |
With their origin in thermodynamics and symbolic dynamics, the Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We will present a framework (through Patterson-Sullivan densities) allowing to get rid of compactness assumptions and survey some applications to the variational principle, the equidistribution of periods, the unique ergodicity of the horospherical foliation and the classification of Gibbs densities on Riemannian covers. This is a joint work with M. Pollicott and B. Schapira. |
| Speakers: |
Prof. Dr. Frédéric Paulin
(Université Paris-Sud 11)
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|
| 28-mar-2012 (wed) |
Peter Bürgisser
|
Prospects for Geometric Complexity Theory
|
15:45-16:45 |
HG G 43 |
| Abstract: |
It is a remarkable fact that two prominent problems of algebraic complexity theory, the permanent versus determinant problem and the tensor rank problem (matrix multiplication), can be restated as explicit orbit closure problems. This offers the potential to prove lower complexity bounds by relying on methods from algebraic geometry and representation theory. While this basic idea for the tensor rank problem goes back to work by Volker Strassen from the mid eighties, the geometric complexity program has gained visibility and momentum in the past years. Some modest lower bounds for border rank have recently been proven by the construction of explicit obstructions. For further progress, a better understanding of irreducible representations of symmetric groups (tensor products and plethysms) is required. Interestingly, asymptotic versions of the the latter questions are of relevance in quantum information theory. |
| Speakers: |
Prof. Dr. Peter Bürgisser
(University of Paderborn, Germany)
|
|
| 4-apr-2012 (wed) |
Péter Varjú
|
Random walks in Euclidean space
|
13:45-14:45 |
HG G 43 |
| Abstract: |
Consider a finite set of isometries of Euclidean space. Take several independent random elements of this set, and compute the image of the origin under their product. This gives rise to a probability distribution on Euclidean space. I will report on a result describing the local behavior of this measure. |
| Speakers: |
Dr. Péter Varjú
(Hebrew University, Jerusalem)
|
|
| 18-apr-2012 (wed) |
Ruth Charney
|
Contracting boundaries of CAT(0) spaces
|
15:45-16:45 |
HG G 43 |
| Abstract: |
Boundaries of hyperbolic spaces play an important role in the study of hyperbolic groups. CAT(0) boundaries are less effective since they are not quasi-isometry invariant and lack some of the nice dynamical properties of hyperbolic boundaries. I will talk about work in progress on a new boundary for CAT(0) spaces which is designed to isolate hyperbolic-like behavior in the visual boundary. |
| Speakers: |
Prof. Dr. Ruth Charney
(Brandeis University, USA, and FIM)
|
|
| 9-may-2012 (wed) |
Tobias Strubel
|
Cross ratios, rigidity and surface group representations
|
15:45-16:45 |
HG G 43 |
| Abstract: |
The classical cross ratio is a well known tool in hyperbolic and projective geometry. In my talk I will survey some rigidity results related with the classical and more general cross ratios. Then I will talk about the recent use of cross ratios in the study of representations of surface groups for Hitchin representations and maximal representations. The latter is a joint work with Tobias Hartnick. |
| Speakers: |
Dr. Tobias Strubel
(Princeton University, USA)
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|
| 16-may-2012 (wed) |
Steffen Weil
|
Aperiodic sequences and aperiodic geodesics
|
15:45-16:45 |
HG G 43 |
| Abstract: |
We will introduce a quantitative condition on orbits of a compact dynamical system which measures aperiodicity. This condition will be discussed concretely for the examples of the Bernoulli-shift and the geodesic flow on compact hyperbolic manifolds. Thereby we will show the existence of special aperiodic sequences and geodesics which are, in some sense, as aperiodic as possible.
This is joint work with V. Schroeder. |
| Speakers: |
Steffen Weil
(Universität Zürich)
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|
| 23-may-2012 (wed) |
Alexander Dranishnikov
|
Essential manifolds and macroscopic dimension
|
15:45-16:45 |
HG G 43 |
| Abstract: |
Gromov introduced the notion of macroscopic dimension to study manifolds with positive scalar curvature. He conjectured that the rational essentiality of an n-manifold implies that its universal cover has macroscopic dimension equal n. We will discuss this and some other related conjectures. |
| Speakers: |
Prof. Dr. Alexander Dranishnikov
(University of Florida, USA, and FIM)
|
|
| 30-may-2012 (wed) |
Virginie Charette
|
Conformally flat Lorentzian 3-manifolds
|
13:00-14:00 |
HG G 43 |
| Abstract: |
A conformally flat Lorentzian manifold is a manifold endowed with a conformal class of Lorentz metrics. Basic examples are Minkowski spacetime and its conformal compactification, the Einstein universe. The Einstein universe is the "universal" conformally flat Lorentzian manifold, in the sense that any such manifold can be shown to develop into the Einstein universe. In this setting, given a discrete group of conformal transformations, one might like to describe a largest domain of discontinuity and its quotient by the group action. In the talk we will discuss certain fundamental domains in dimension 3 bounded by "crooked surfaces", which are objects introduced by Drumm for Minkowski spacetime, and generalized to the Einstein universe by Frances. |
| Speakers: |
Prof. Dr. Virginie Charette
(Université de Sherbrooke, Canada)
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