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Autumn Semester 2015

Date / Time Speaker Title Location
7 October 2015
15:45-16:45 		Yash Lodha
EPF Lausanne
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Geometry Seminar

Title Nonamenable finitely presented groups of piecewise projective homeomorphisms
Speaker, Affiliation Yash Lodha, EPF Lausanne
Date, Time 7 October 2015, 15:45-16:45
Location HG G 43
Abstract Monod introduced examples of groups of piecewise projective homeomorphisms, which he demonstrated are non amenable despite the fact that they do not contain non abelian free subgroups. In joint work with Justin Moore, I isolated examples of finitely presented groups of piecewise projective homeomorphisms with the same property. These groups are also of type F_{\infty}. In recent work with Burillo and Reeves, we investigated the normal subgroup structure of these groups. In this talk I will present a survey of these groups and discuss their striking properties.
Nonamenable finitely presented groups of piecewise projective homeomorphismsread_more
HG G 43
21 October 2015
15:45-16:45 		Conrad Plaut
University of Tennessee, Knoxville
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Geometry Seminar

Title Applications of Discrete Homotopy Theory
Speaker, Affiliation Conrad Plaut, University of Tennessee, Knoxville
Date, Time 21 October 2015, 15:45-16:45
Location HG G 43
Abstract I will give an introduction to discrete homotopy theory developed by Berestovskii, Wilkins, and myself, which uses discrete chains and homotopies rather than continuous paths and traditional homotopies. Not only do these methods allow one to understand topology at a given scale, the discrete nature allows one to use counting arguments to control quantities related to the fundamental group. Applications include a quantitative, generalized version of Gromov’s Theorem about generators of the fundamental group of a compact manifold; a “curvature free” fundamental group finiteness theorem generalizing those of M. Anderson and Shen-Wei; as well as giving a complete understanding of the “closure” of the collection of $\delta$-covers in the sense of Sormani-Wei. The quantities involved depend on the metric, but there are also metric-free methods that lead to new topological invariants.
Applications of Discrete Homotopy Theoryread_more
HG G 43
28 October 2015
15:45-16:45 		Sergei Buyalo
Steklov Mathematical Institute
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Geometry Seminar

Title Moebius and Sub-Moebius structures on boundaries of hyperbolic spaces
Speaker, Affiliation Sergei Buyalo, Steklov Mathematical Institute
Date, Time 28 October 2015, 15:45-16:45
Location HG G 43
Abstract It will be explained that on the boundary at infinity X of every Gromov hyperbolic space Y there is a Moebius structure M, which is invariant under isometries of Y, such that the M-topology on X coincides with the standard topology. Furthermore, under some assumption on the isometry group of Y, the Moebius structure M can be deformed into a ptolemaic one with the same properties.
Moebius and Sub-Moebius structures on boundaries of hyperbolic spacesread_more
HG G 43
4 November 2015
15:45-16:45 		Robert Kucharczyk
ETH Zurich
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Geometry Seminar

Title Modular embeddings for Fuchsian groups
Speaker, Affiliation Robert Kucharczyk , ETH Zurich
Date, Time 4 November 2015, 15:45-16:45
Location HG G 43
Abstract Among lattices in SL(2,R) the arithmetic ones are the most well-studied. In this talk I will present some examples of lattices that are not arithmetic but share many properties with arithmetic ones, by virtue of so-called modular embeddings. These are certain equivariant holomorphic maps that relate these non-arithmetic groups with some arithmetic lattices of higher rank. Special emphasis will be laid on the algebro-geometric properties of the curves that are uniformised by these non-arithmetic groups.
Modular embeddings for Fuchsian groupsread_more
HG G 43
11 November 2015
15:45-16:45 		Lukas Parapatits
ETH Zurich
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Geometry Seminar

Title Simple Translation-Invariant Valuations
Speaker, Affiliation Lukas Parapatits, ETH Zurich
Date, Time 11 November 2015, 15:45-16:45
Location HG G 43
Abstract I will discuss a new classification of simple translation-invariant valuations on polytopes that does not assume any regularity at all. As a corollary one can derive the well-known conditions for translative-equidecomposability of two polytopes. Here, two polytopes are said to be translative-equidecomposable if it is possible to cut them up into essentially (up to translations) the same pieces. Another consequence is a unified and simplified proof of classifications of continuous simple translation-invariant valuations on convex bodies by Klain and Schneider. This is a joint work with Katharina Kusejko.
Simple Translation-Invariant Valuationsread_more
HG G 43
18 November 2015
15:45-16:45 		Alexander Lytchak
Universität Köln
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Geometry Seminar

Title Classical Plateau problem in non-classical spaces
Speaker, Affiliation Alexander Lytchak, Universität Köln
Date, Time 18 November 2015, 15:45-16:45
Location HG G 43
Abstract The question of Plateau concerns the existence of soap films: objects of minimial area spanning a given curve in the Euclidean spaces. The most classical answer to this question has been provided by Rado and Douglas and proves the existence of parametrized discs of minimal area spanning an arbitrary Jordan curve. The result was generalized by Morrey to Riemannian manifolds. In the talk I will discuss a solution of the Plateau problem in arbitrary metric spaces, regularity of the solutions and some applications to isoperimetric problems.
Classical Plateau problem in non-classical spacesread_more
HG G 43
2 December 2015
15:45-16:45 		Mentor Stafa
ETH Zurich
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Geometry Seminar

Title Spaces of commuting elements in Lie groups
Speaker, Affiliation Mentor Stafa, ETH Zurich
Date, Time 2 December 2015, 15:45-16:45
Location HG G 43
Abstract The spaces of group homomorphisms Hom(A,B) have been studied in various contexts. We study the space of pairwise commuting n-tuples in a compact and connected Lie group G, from the topological viewpoint. We will give a brief survey of recent work on these spaces as well as tools to compute their homology with certain coefficients, possibly the ring of integers. Among the tools are various stable decompositions of spaces of homomorphisms into the wedge sum of smaller spaces.
Spaces of commuting elements in Lie groupsread_more
HG G 43
9 December 2015
15:45-16:45 		Victor Chepoi
Université de la Méditerranée, Marseille
Details

Geometry Seminar

Title Helly graphs: local-to-global characterization and bicombing
Speaker, Affiliation Victor Chepoi, Université de la Méditerranée, Marseille
Date, Time 9 December 2015, 15:45-16:45
Location HG G 43
Abstract In this talk, we will provide a local-to-global characterization of Helly graphs as graphs in which the clique complex is simply connected and the set of maximal cliques satisfies the Helly property. As an example of Helly graphs, we will consider thickening of swm-graphs with respect to Boolean gated subgraphs (which are dual polar spaces). swm-Graphs extend median graphs (1-skeleta of CAT(0) cube complexes). As a second result, we will show that Helly groups (i.e., groups acting geometrically on Helly graphs) are biautomatic. The talk is based on a joint work wirh J. Chalopin, D. Osajda, and H. Hirai.
Helly graphs: local-to-global characterization and bicombingread_more
HG G 43
16 December 2015
15:45-16:45 		Adrien Le Boudec
Université Paris-Sud 11
Details

Geometry Seminar

Title C*-simplicity and the amenable radical
Speaker, Affiliation Adrien Le Boudec, Université Paris-Sud 11
Date, Time 16 December 2015, 15:45-16:45
Location HG G 43
Abstract We will first survey recent results of Kalentar-Kennedy and Breuillard-Kalentar-Kennedy-Ozawa about the connection between C*-simplicity of a discrete countable group and its boundary actions. We will then explain the construction of non-C*-simple groups with no amenable normal subgroup. These groups are defined in terms of an action on a tree, and some examples arising from this construction are moreover finitely generated and simple.
C*-simplicity and the amenable radicalread_more
HG G 43

Organisers: Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Viktor Schröder, Alessandro Sisto

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

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