Geometry seminar

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Autumn Semester 2013

Date / Time

Speaker

Title

Location

25 September 2013
15:45-16:45

Dr. Benjamin Matschke
FIM, ETH Zürich

Event Details

Geometry Seminar

Title	Center point and Tverberg theorems in projective space
Speaker, Affiliation	Dr. Benjamin Matschke, FIM, ETH Zürich
Date, Time	25 September 2013, 15:45-16:45
Location	HG G 43
Abstract	Three classic topics in discrete geometry are the ham sandwich theorem, the center point theorem, and Tverberg's theorem. This talk is about a common generalization, which lives in projective space. This is joint work with Roman Karasev.

Center point and Tverberg theorems in projective spaceread_more

HG G 43

2 October 2013
15:45-16:45

Alessandro Sisto

Event Details

Geometry Seminar

Title	Relative hyperbolicity vs thickness of (random) right-angled Coxeter groups
Speaker, Affiliation	Alessandro Sisto,
Date, Time	2 October 2013, 15:45-16:45
Location	HG G 43
Abstract	Relatively hyperbolic groups form a rich class of groups which generalises hyperbolic groups, while thick groups are "built-up" in a certain inductive way which prevents them from being relatively hyperbolic in a non-trivial way. Right-angled Coxeter groups are hyperbolic relative to thick parabolic subgroups (in the Coxeter sense). Moreover, this canonical relatively hyperbolic structure can be detected algorithmically and reasonably fast from the graph describing a given right-angled Coxeter group. I will also discuss theorems and data from computer experiments on the relative hyperbolicity or thickness of right-angled Coxeter groups arising from random graphs. Based on joint work with Jason Behrstock, Pierre-Emmanuel Caprace and Mark Hagen.

Relative hyperbolicity vs thickness of (random) right-angled Coxeter groupsread_more

HG G 43

9 October 2013
15:45-16:45

Sebastian Baader
Universität Bern

Event Details

Geometry Seminar

Title	Geometric signature of surfaces
Speaker, Affiliation	Sebastian Baader, Universität Bern
Date, Time	9 October 2013, 15:45-16:45
Location	HG G 43

Geometric signature of surfaces

HG G 43

23 October 2013
15:45-16:45

Alex Lubotzky
Einstein institute of Mathematics, Israel

Event Details

Geometry Seminar

Title	Arithmetic quotients of the mapping class group
Speaker, Affiliation	Alex Lubotzky, Einstein institute of Mathematics, Israel
Date, Time	23 October 2013, 15:45-16:45
Location	HG G 43
Abstract	Let M=M(g) be the mapping class group of a surface of genus g > 1. As it is well known, it is mapped onto the symplectic group Sp(2g,Z). We will show that this is only a first case in a series: in fact, for every pair (S,r) when S is a finite group with less than g generators and r is a Q-irreducible representation of S, we associate an arithmetic group which is then shown to be a virtual quotient of M. The case when S is the trivial group gives the above Sp(2g,Z) but many new quotients are obtained. For example it is used to show that M(2) is virtually mapped onto a non-abelian free group. Another application is an answer to a question of Kowalski, showing that generic elements in the Torelli groups are hyperbolic and fully irreducible. Joint work with Fritz gruenwald, Michael Larsen and Justin Malestein.

Arithmetic quotients of the mapping class groupread_more

HG G 43

30 October 2013
15:45-16:45

Brian Bowditch
University of Warwick, UK

Event Details

Geometry Seminar

Title	Coarse median spaces
Speaker, Affiliation	Brian Bowditch, University of Warwick, UK
Date, Time	30 October 2013, 15:45-16:45
Location	HG G 43
Abstract	We describe the notion of a ``coarse median'' on a geodesic metric space. This satisfies the axioms of a median algebra up to bounded distance. The existence of a coarse median is invariant under quasi-isometry and might be thought of as a kind of coarse non-positive curvature condition. One can define a ``coarse median group'' as a finitely generated group whose Cayley graph admits a coarse median. This property is closed under direct products and relative hyperbolicity. Examples are hyperbolic groups and right-angled Artin groups. Using the centroid construction of Behrstock and Minsky, one sees that the mapping class group of a compact surface is coarse median. I aim to describe the general background to this topic, and give some examples of applications.

Coarse median spacesread_more

HG G 43

6 November 2013
15:45-16:45

John MacKay
University of Bristol

Event Details

Geometry Seminar

Title	Quasi-arcs and quasi-circles
Speaker, Affiliation	John MacKay, University of Bristol
Date, Time	6 November 2013, 15:45-16:45
Location	HG G 43
Abstract	In 1963, Ahlfors gave a simple geometric characterisation of those planar Jordan curves that are the images of a quasi-conformal homeomorphism of the plane. Generalised to a metric space setting, these quasi-circles have applications to the study of hyperbolic and relatively hyperbolic groups. We will discuss existence results for such curves and applications. (Partly based on joint work with Alessandro Sisto.)

Quasi-arcs and quasi-circlesread_more

HG G 43

13 November 2013
15:45-16:45

Sergei Buyalo
Steklov Inst. St. Petersburg

Event Details

Geometry Seminar

Title	Moebius characterization of the boundary of rank one symmetric spaces
Speaker, Affiliation	Sergei Buyalo, Steklov Inst. St. Petersburg
Date, Time	13 November 2013, 15:45-16:45
Location	HG G 43
Abstract	A M\"obius space (on a set X) is a class of metrics having the same cross-ratios. A M\"obius space is ptolemaic if it is invariant under inversion operations. The boundary at infinity of a CAT(-1) space is in a natural way a M\"obius space, which is ptolemaic. We give a free of classification proof of the following result that characterizes the rank one symmetric spaces of noncompact type purely in terms of their M\"obius geometry: Let X be a compact Ptolemy space which contains a Ptolemy circle and allows many space inversions. Then X is M\"obius equivalent to the boundary at infinity of a rank one symmetric space.

Moebius characterization of the boundary of rank one symmetric spacesread_more

HG G 43

20 November 2013
15:45-16:45

Piotr Przytycki
Polish Academy of Sciences

Event Details

Geometry Seminar

Title	Cocompact cubulations of graph manifolds
Speaker, Affiliation	Piotr Przytycki, Polish Academy of Sciences
Date, Time	20 November 2013, 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 (CANCELLED)

HG G 43

27 November 2013
15:45-16:45

Giannis Platis
University of Crete

Event Details

Geometry Seminar

Title	Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1
Speaker, Affiliation	Giannis Platis, University of Crete
Date, Time	27 November 2013, 15:45-16:45
Location	HG G 43
Abstract	We use generalised cross–ratios to prove the Ptolemaean inequality and the Theorem of Ptolemaeus in the setting of the boundary of symmetric Riemannian spaces of rank 1 and of negative curvature.

Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1read_more

HG G 43

4 December 2013
15:45-16:45

Cristina Pagliantini
ETH Zürich

Event Details

Geometry Seminar

Title	Simplicial volume vs integral (foliated) simplicial volume
Speaker, Affiliation	Cristina Pagliantini, ETH Zürich
Date, Time	4 December 2013, 15:45-16:45
Location	HG G 43
Abstract	Gromov conjectured that an aspherical oriented closed connected manifold with vanishing simplicial volume has null Euler characteristic. When the simplicial volume is replaced by the integral foliated simplicial volume, the corresponding statement is true. It follows that it is interesting to understand the relation between simplicial volume and the integral foliated one for aspherical manifolds. We show that they are equal for closed hyperbolic 3-manifolds. Joint work with Clara Löh.

Simplicial volume vs integral (foliated) simplicial volumeread_more

HG G 43

18 December 2013
15:45-16:45

Marco Spinaci
Université de Grenoble I

Event Details

Geometry Seminar

Title	Deformations of twisted harmonic maps and variation of the energy
Speaker, Affiliation	Marco Spinaci, Université de Grenoble I
Date, Time	18 December 2013, 15:45-16:45
Location	HG G 43
Abstract	The properties of the moduli space of Higgs bundles on a compact Riemann surface, constructed by N. Hitchin in 1987, have been the subject of several works. Among these, C. Simpson in 1994 gave a generalization of the construction of this moduli space replacing the Riemann surface with a projective manifold. However, the study of the functional given by the energy of the Higgs field (that is more generally defined on the moduli space of representations of the fundamental group of any Riemannian manifold) has not been systematically developed in higher dimension. After recalling the main ideas of the correspondence between representations and Higgs bundles, in this talk we propose an approach of such a study via the theory of deformations of twisted harmonic maps, up to the second order. This theory allows us to obtain formulas fo the variations of the energy, thanks to which we can prove the identification between critical points of the energy and polarized complex variations of Hodge structure. We can also prove that the energy is a Kähler potential for the natural complex structure and finally compute the eigenvalues of the Hessian of the energy.

Deformations of twisted harmonic maps and variation of the energyread_more

HG G 43

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

Archive: 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