Geometry/Topology Seminar
Thursdays at 3:00PM
in Eckhart 206.
Fall 1999
- Oct 7, at 3:00PM
- V. Mathai, University of Adelaide
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
- Vadim Kaloshin, Princeton University
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
For questions, contact