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Autumn Semester 2009

Date / Time Speaker Title Location
7 October 2009
15:45-17:15 		Uri Bader
Department of Mathematics, Technion Haifa, Israel
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Geometry Seminar

Title The generalized Weyl group and applications to rigidity
Speaker, Affiliation Uri Bader, Department of Mathematics, Technion Haifa, Israel
Date, Time 7 October 2009, 15:45-17:15
Location HG G 43
Abstract Classically, associated with every algebraic group there is a finite group - the Weyl group - which carries a certain amount of information about the algebraic group. I will explain how one can associate a "generalized Weyl group" with every discrete group in a way "compatible" with the classical one (e.g the Weyl group of SL_3(Z) will be S_3), and how some information about the representation theory of a group is encoded in its Weyl group. I will give some example resulting in proving some rigidity properties of groups. The talk is based on a joint work with Alex Furman.
The generalized Weyl group and applications to rigidityread_more
HG G 43
14 October 2009
15:45-17:15 		Prof. Dr. Omri Sarig
Department of Mathematics, Penn State University
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Geometry Seminar

Title Equidistribution of horocycles on abelian covers of compact hyperbolic surfaces
Speaker, Affiliation Prof. Dr. Omri Sarig, Department of Mathematics, Penn State University
Date, Time 14 October 2009, 15:45-17:15
Location HG G 43
Abstract A point is called generic for a flow preserving an infinite ergodic invariant Radon measure, if its orbit satisfies the conclusion of the ratio ergodic theorem for every pair of continuous functions with compact support and non-zero integrals. This means, roughly, that the relative time the orbit spends inside a nice set A tends to zero, but that the ratio of the times the orbit spends in two "nice" sets A,B tends to a definite limit, equal to the ratio of the measures of A and B. The generic points for horocycle flows on hyperbolic surfaces of finite genus are understood, but there are no results in infinite genus. We give such a result, by characterizing the generic points for Z^d--covers. This is joint work with B. Schapira.
Equidistribution of horocycles on abelian covers of compact hyperbolic surfacesread_more
HG G 43
21 October 2009
15:45-17:15 		Prof. Dr. Sergei Buyalo
St.Petersburg Department of V. A. Steklov, Institute of Mathematics of the Russian Academy of Sciences
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Geometry Seminar

Title Boundary at infinity of symmetric rank one spaces
Speaker, Affiliation Prof. Dr. Sergei Buyalo, St.Petersburg Department of V. A. Steklov, Institute of Mathematics of the Russian Academy of Sciences
Date, Time 21 October 2009, 15:45-17:15
Location HG G 43
Boundary at infinity of symmetric rank one spaces
HG G 43
28 October 2009
15:45-17:15 		Uri Shapira
Einstein Institute of Mathematics, Hebrew University of Jerusalem
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Geometry Seminar

Title Homogeneous orbit closures and Diophantine approximations of algebraic numbers
Speaker, Affiliation Uri Shapira, Einstein Institute of Mathematics, Hebrew University of Jerusalem
Date, Time 28 October 2009, 15:45-17:15
Location HG G 43
Abstract The content of the talk is a joint work with Elon Lindenstrauss. In homogeneous dynamics one studies the action of a group A on the homogeneous space G/H. Usually G is a Lie group and A,H are closed subgroups of G (in our discussion H will be a lattice in G). I will be interested in my talk in points, x, of G/H for which the closure of the orbit Ax is itself an orbit of a (possibly bigger) group A'2). These examples are connected to number theory, and as an application of the A-regularity we obtain some new information on the Diophantine properties of algebraic numbers. I will NOT assume the audience is familiar with the subject hence everyone is welcome.
Homogeneous orbit closures and Diophantine approximations of algebraic numbersread_more
HG G 43
4 November 2009
15:45-17:15
Details

Geometry Seminar

Title No Seminar
Speaker, Affiliation
Date, Time 4 November 2009, 15:45-17:15
Location HG G 43
No Seminar
HG G 43
11 November 2009
15:45-17:15 		Ruth Charney
Brandeis University, Waltham, MA
Details

Geometry Seminar

Title Right-angled Artin groups and their Automorphisms
Speaker, Affiliation Ruth Charney, Brandeis University, Waltham, MA
Date, Time 11 November 2009, 15:45-17:15
Location HG G 43
Abstract Associated to any Coxeter group is an infinite group known as an Artin group. The Artin groups associated to right-angled Coxeter groups have proved to be particularly interesting from both an algebraic and geometric viewpoint. We will discuss these groups, their automorphism groups, and their associated geometries.
Right-angled Artin groups and their Automorphismsread_more
HG G 43
18 November 2009
15:45-17:15
Details

Geometry Seminar

Title No Seminar
Speaker, Affiliation
Date, Time 18 November 2009, 15:45-17:15
Location HG G 43
No Seminar
HG G 43
25 November 2009
15:45-17:15 		John Mackay
University of Illinois at Urbana-Champaign
Details

Geometry Seminar

Title Spaces and groups with conformal dimension greater than one
Speaker, Affiliation John Mackay, University of Illinois at Urbana-Champaign
Date, Time 25 November 2009, 15:45-17:15
Location HG G 43
Abstract The conformal dimension of a metric space is a quasi-symmetric invariant that in some sense measures the `best shape' of the metric space under quasi-symmetric deformations. In this talk I'll survey some known results about conformal dimension and give examples where this invariant is interesting, such as the boundary at infinity of a Gromov hyperbolic group, paying particular attention to spaces of topological dimension one. I'll also give a lower bound greater than one for the conformal dimension of a natural class of metric spaces that includes boundaries of hyperbolic groups that are connected with no local cut points.
Spaces and groups with conformal dimension greater than one read_more
HG G 43
2 December 2009
15:45-16:45 		Marco Abate
Università di Pisa
Details

Geometry Seminar

Title Poincaré-Bendixson theorems for meromorphic connections and homogeneous vector fields
Speaker, Affiliation Marco Abate, Università di Pisa
Date, Time 2 December 2009, 15:45-16:45
Location HG G 43
Abstract Time-1 maps of homogeneous vector fields provide important examples of holomorphic maps tangent to the identity; for instance Camacho has proved that in dimension 1 every holomorphic germ tangent to the identity is locally topologically conjugated to such a time-1 map. In this talk I shall present some powerful techniques useful for the study of the dynamics of homogeneous vector fields in dimension two (and possibly higher), reducing the study of integral curves of the vector field to the study of geodesics for a meromorphic connection on the projective line. Two main results are: a Poincaré-Bendixson theorem describing the recurrence behavior of such geodesics, and hence of the integral curves; and a list of formal and holomorphic local normal forms allowing a detailed study of the dynamics nearby the poles of the connection. As a consequence we get new examples showing unexpected behaviors, and we get a complete description of the dynamics for a large family of such fields---and thus of the corresponding time-1 maps, providing the first complete description of the dynamics in a full neighbourhood of the origin for a large class of holomorphic germs tangent to the identity in dimension two. (Joint work with F. Tovena)
Poincaré-Bendixson theorems for meromorphic connections and homogeneous vector fieldsread_more
HG G 43
9 December 2009
15:45-16:45 		Viktor Schroeder
Details

Geometry Seminar

Title A Moebius Characterization of the Heisenberg Group
Speaker, Affiliation Viktor Schroeder,
Date, Time 9 December 2009, 15:45-16:45
Location HG G 43
A Moebius Characterization of the Heisenberg Group
HG G 43
16 December 2009
15:45-16:45 		Jeremy Tyson
University of Illinois at Urbana-Champaign
Details

Geometry Seminar

Title Dimensions of self-similar fractals in Carnot groups
Speaker, Affiliation Jeremy Tyson, University of Illinois at Urbana-Champaign
Date, Time 16 December 2009, 15:45-16:45
Location HG G 43
Abstract We consider self-similar iterated function systems (IFS) in a Carnot group equipped with a Carnot-Carathéodory (CC) metric. Contractive similarity maps of Carnot groups are compositions of left translations and contractive dilations. Inspired by work of Falconer, Solomyak and Falconer--Miao, we establish almost sure dimension formulas for parameterized families of CC self-similar IFS and give quantitative estimates for the size of the exceptional sets of parameters for which our dimension formula fails. As a consequence, we show that CC self-similar subsets are almost surely horizontal: their CC dimension is minimal relative to their Euclidean dimension. As a byproduct we obtain precise estimates for the dimensions of such sets with respect to the underlying Euclidean geometry, where they arise as invariant sets for highly nonlinear, nonconformal IFS. This talk is based on joint work with Zoltán Balogh, Ben Warhurst, Reto Berger and Roberto Monti.
Dimensions of self-similar fractals in Carnot groupsread_more
HG G 43

Organisers: Theo Bühler, Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Enrico Le Donne, 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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