# Geometry/Topology Seminar

Thursdays at 3:00PM in Eckhart 206.

## Fall 1999

Oct 7, at 3:00PM
The Quantum Hall Effect
Oct 14, at 3:00PM
Chris Connell, UIC
Minimal entropy rigidity in finite volume
Oct 21
Damien Gaboriau, ENS, Lyon
Cost of equivalence relations and discrete groups

Abstract:
Let an infinite discrete group $\Gamma$ act freely and ergodically in a probability preserving way on a standard Borel space. Forget the action and the group, and just look at the equivalence relation : {\it to be in the same orbit}. What kind of information does the relation remember ? For example, the relation remembers if $\Gamma$ is amenable or not, and by a theorem by Ornstein-Weiss, any additionnal structure is lost: Any two free ergodic actions of infinite amenable groups have isomorphic orbit partitions. In non-amenable situations, one has some {\it rigidity results} (R.~Zimmer, A.~ Furman) essentially related to {\it higher rank} lattices. We present a numerical invariant of groups {\it the cost}, whose value is in general the same for groups with isomorphic orbit partitions, and we compute it for a wide class of groups. For instance, for the free group $F_p$ on $p$ generators ($p\geq 2$), or $F_q$ ($q>p$), or $SL(2,\bold Z)$, or $F_n\times F_q$ the value of the cost being respectively $p$, $q$, $1+{1\over 12}$ and $1$, these groups cannot define isomorphic orbit partitions.
Oct 28, at 3:00PM
Amie Wilkinson, Northwestern
Partially Hyperbolic diffeomorphisms

Nov 4, at 4:30PM,   Joint topology/geometry/algebraic geometry seminar
Amnon Neeman
Smirnov's work on the standard conjectures
Nov 11 at 3:00PM
Giovanni Forni, Princeton
Proof of a conjecture of Kontsevich and Zorich on the Lyapunov exponents of the Teichmuller flow and applications.
Nov 17 (special day)
Edward Turner, SUNY at Albany
Fixed points of endomorphisms of (mostly free) groups
Nov 18
Harvey Friedman, Ohio State
Semilinear dynamics; chains of algebraic sets.

Nov 24 (special day and time), at 1:30 PM
Generic diffeomorphisms with superexponential growth of the number of periodic points.
Nov 30, at 3:00PM in Eck 312 (special day and time)
Andrzej Zuk, ENS-Lyon
Generic Hyperbolic groups with property (T).

Abstract:
Property (T) is a property of unitary representations of groups. It was used to solve several important problems related to different branches of mathematics like lattices in Lie groups, expanding graphs, invariant measures on spheres and operator algebras. We give a simple condition for a discrete group to have Kazhdan's property (T). This condition is easy to check and gives Kazhdan constants. We give examples of groups to which this method applies. We show that generic finitely presented groups in the sense of Gromov satisfy this condition and thus have property (T). Moreover we prove that small changes in the presentation of a group satisfying this condition do not change the fact that the group has property (T).
Dec 2
Danny Calegari, UC Berkeley
Taut foliations (are?) transverse to product structures.
January 13
Tom Nevins, University of Chicago
Moduli spaces of framed vector bundles on ruled surfaces
January 20
Lev Birbrair, Brazil
Metric Geometry and Real Algebraic Singularities.
January 27
Dmitry Jakobson, University of Chicago
Geodesic flows and limits of eigenfunctions
February 2, at 4:00PM (special day and time)
Alex Lubotzky
TBA
February 10
John Stallings, UC Berkeley
TBA
March 9
Boris Goldfarb,
TBA

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