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Spring Semester 2014

Date / Time Speaker Title Location
26 February 2014
15:45-16:45 		Amir Mohammadi
University of Texas at Austin
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Geometry Seminar

Title Unipotent flows on infinite volume manifolds
Speaker, Affiliation Amir Mohammadi, University of Texas at Austin
Date, Time 26 February 2014, 15:45-16:45
Location HG G 43
Abstract Unipotent flows on homogeneous spaces obtained as quotients of a Lie group by a lattice have been extensively studied over the past 40 years or so, with several fundamental applications. Starting from the late 80's there have been several results aiming at extending some of these results to certain infinite volume settings. However, our understanding of the subject, beyond the horospherical foliation in the rank one case, is rather poor. In this talk we will discuss some, ongoing, attempts in this direction. This is a joint project with Hee Oh.
Unipotent flows on infinite volume manifoldsread_more
HG G 43
5 March 2014
15:45-16:45 		Piotr Przytycki
Polish Academy of Sciences
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Geometry Seminar

Title Cocompact cubulations of graph manifolds
Speaker, Affiliation Piotr Przytycki, Polish Academy of Sciences
Date, Time 5 March 2014, 15:45-16:45
Location HG G 43
Abstract Let M be a graph manifold. We show that the fundamental group of M is the fundamental group of a compact nonpositively curved cube complex if and only if M is chargeless, that is in each block there is a horizontal surface whose boundary circles are vertical in adjacent blocks. This is joint work with Mark Hagen.
Cocompact cubulations of graph manifoldsread_more
HG G 43
12 March 2014
15:45-16:45 		George Willis
The University of Newcastle, New South Wales, Australia
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Geometry Seminar

Title The structure lattice of locally normal subgroups of a totally disconnected locally compact group
Speaker, Affiliation George Willis, The University of Newcastle, New South Wales, Australia
Date, Time 12 March 2014, 15:45-16:45
Location HG G 43
Abstract The structure lattice of a totally disconnected locally compact group G is a local invariant, that is, it may be determined from any compact open subgroup of G. Properties of the structure lattice reflect the structure of G and each compactly generated and topologically simple group may be classified as being of one of several types according to these properties. For example, compact totally disconnected groups are profinite and one type of simple group has compact open subgroups that are hereditarily just-infinite profinite groups. The structure lattice and examples, where they are known, of the various types of topologically simple groups will be described. This is joint work with Pierre-Emmanuel Caprace and Colin Reid.
The structure lattice of locally normal subgroups of a totally disconnected locally compact groupread_more
HG G 43
26 March 2014
15:45-16:45 		Petra Schwer
Universität Münster
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Geometry Seminar

Title Curvature of braid groups
Speaker, Affiliation Petra Schwer, Universität Münster
Date, Time 26 March 2014, 15:45-16:45
Location HG G 43
Abstract We will present the notion of a CAT(0) and more generally CAT(k)-space which are spaces with certain upper curvature bounds. While these curvature properties are in general hard to verify one can deduce many algebraic properties of a group from an action on such a space. We show that braid groups with at most 6 strands are CAT(0), i.e. act geometrically on a CAT(0) space, using the close connection between these groups, the associated non-crossing partition complexes and the embeddability of their diagonal links into spherical buildings.
Curvature of braid groupsread_more
HG G 43
9 April 2014
15:45-16:45 		Anne Parreau
Université de Grenoble 1
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Geometry Seminar

Title Surface groups acting on A_2-buildings, invariant trees and surfaces
Speaker, Affiliation Anne Parreau, Université de Grenoble 1
Date, Time 9 April 2014, 15:45-16:45
Location HG G 43
Abstract We study representations of a punctured surface group in PGL(3) over a non archimedean field, acting on the associated euclidean building X. Under simple conditions on Fock-Goncharov generalized shearing parameters, we show that the action preserves a weakly convex subcomplex in X, which is piecewise a surface or a tree. It allows to describe explicitly a large family of degenerations of convex projective structures on the surface.
Surface groups acting on A_2-buildings, invariant trees and surfacesread_more
HG G 43
16 April 2014
15:45-16:45 		Anne Thomas
University of Glasgow
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Geometry Seminar

Title Quasi-isometry classification of certain right-angled Coxeter groups
Speaker, Affiliation Anne Thomas, University of Glasgow
Date, Time 16 April 2014, 15:45-16:45
Location HG G 43
Abstract We investigate the quasi-isometry classification of 2-dimensional right-angled Coxeter groups. We determine which such groups split over virtually cyclic subgroups and which are quasi-isometric to the hyperbolic plane. Our main result uses Bowditch's JSJ decomposition of one-ended hyperbolic groups to give a complete classification of an infinite family. From this and a theorem of Crisp and Paoluzzi, it follows that for these groups, quasi-isometry is weaker than commensurability. This is joint work with Pallavi Dani.
Quasi-isometry classification of certain right-angled Coxeter groupsread_more
HG G 43
30 April 2014
15:45-16:45 		Daniele Alessandrini
Universität Heidelberg
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Geometry Seminar

Title Thurston's asymmetric metric for unusual surfaces
Speaker, Affiliation Daniele Alessandrini, Universität Heidelberg
Date, Time 30 April 2014, 15:45-16:45
Location HG G 43
Abstract Thurston introduced its asymmetric metric for Teichmüller spaces of closed surfaces or for surfaces with punctures. This distance has very nice geometric properties and applications. Similar distances can be defined also for the Teichmüller spaces of surfaces with boundary and of surfaces of infinite topological type, even if these cases are much more delicate. I will discuss some properties of this distance in this more general setting.
Thurston's asymmetric metric for unusual surfacesread_more
HG G 43
14 May 2014
15:45-16:45 		Viktor Schroeder
Universität Zürich
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Geometry Seminar

Title Moebius structure on the boundary of complex hyperbolic space
Speaker, Affiliation Viktor Schroeder, Universität Zürich
Date, Time 14 May 2014, 15:45-16:45
Location HG G 43
Abstract The boundary at infinity of the complex hyperbolic space carries a natural Moebius structure. We characterize this Moebius structure purely in terms of metric Moebius geometry. This is joint work with S. Buyalo.
Moebius structure on the boundary of complex hyperbolic spaceread_more
HG G 43
21 May 2014
15:45-16:45 		Menny Aka
EPF Lausanne
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Geometry Seminar

Title Points on spheres and their orthogonal lattices
Speaker, Affiliation Menny Aka, EPF Lausanne
Date, Time 21 May 2014, 15:45-16:45
Location HG G 43
Abstract It is a classical question to understand the distribution (when projected to the unit sphere) of the solutions of x^2+y^2+z^2=D as D grows. To each such solution v we further attach the lattice obtained by intersecting the hyperplane orthogonal to v with the set of integral vectors. This way, we obtain, for any D that can be written as a sum of three squares, a finite set of pairs consisting of a point on the unit sphere and a lattice. In the talk I will discuss a joint work with Manfred Einsiedler and Uri Shapira which considers the joint distribution of these pairs in the appropriate spaces. I will outline a general approach to such problems and discuss dynamical input needed to establish that these pairs distribute uniformly.
Points on spheres and their orthogonal latticesread_more
HG G 43

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

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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