FALL 2000

DATE

SEMINAR

TIME

ROOM

SPEAKER

TITLE

Th Sep 7

topology / geometry

12:00-1:00

RH 142

Bryan Clair

L2 - Invariants

Abstract: Let X be a compact manifold or cell complex, and \tilde{X} be an infinite covering space with group of deck transformations G. By studying L2-forms (or cochains) on \tilde{X}, one can define topological invariants of X. The most classical of these are the L2 Betti numbers, first considered by Atiyah in 1976. Like the ordinary Betti numbers of a compact space, the L2 Betti numbers are the dimension of a homology group. However, the homology groups coming from L2 -forms are infinite dimensional Hilbert spaces, so the machinery of von Neumann algebras is needed to provide a quantitative dimension.

I will spend the first lecture on background material, and basic examples, with some older theorems and big conjectures thrown in for spice. Don't worry if you don't know anything about von Neumann algebras. I plan to talk about Gromov's result that the L2 Betti numbers vanish when X is aspherical and G is amenable. I'll prove Luck's theorem, which says that ordinary Betti numbers (renormalized) of a tower of covering spaces converge to the L2 Betti numbers of the limit covering. I will also discuss more refined L2 invariants such as the Novikov-Shubin invariants and L2 -Reidemeister torsion.

Th Sep 7

topology/ analysis

2:10-3:00

RH 202

Kevin Scannell

Topological Groups acting on Hyperbolic Space

Abstract: We will study topological groups as they act on hyperbolic groups. We are interested in Bianchi Groups, Selberg trace formula etc. The book we will be using is by Elstrodt, Grunewald and Mennicke and is published by Springer Verlag.

Th Sep 14

topology / geometry

12:00-1:00

RH 142

Bryan Clair

L2 - Invariants - Continued

Th Sep 14

topology/ analysis

2:10-3:00

RH 202

Anneke Bart

Topological Groups acting on Hyperbolic Space

Abstract: We will start in Chapter 3 by discussing Poincare Series. In particular, we will go over the three main examples given in the book.

Th Sep 21

topology / geometry

12:00-1:00

RH 142

Bryan Clair

L2 - Invariants - Continued

Th Sep 21

topology/ analysis

2:10-3:00

RH 202

Anneke Bart

Topological Groups acting on Hyperbolic Space

Th Sep 28

topology / geometry

12:00-1:00

RH 142

Bryan Clair

L2 - Invariants - Continued

Th Sep 28

topology/ analysis

2:10-3:00

RH 202

Anneke Bart

Topological Groups acting on Hyperbolic Space

Tu Oct 3

algebra

3:10-4:00

RH 134

Greg Marks

Baer Rings and 2-Primal Rings I

Th Oct 5

topology / geometry

12:00-1:00

RH 142

Bryan Clair

L2 - Invariants - Continued

Th Oct 5

topology/ analysis

2:10-3:00

RH 202

Anneke Bart

Topological Groups acting on Hyperbolic Space

Tu Oct 10

algebra

3:10-4:00

RH 134

Greg Marks

Baer Rings and 2-Primal Rings II

Th Oct 12

topology / geometry

12:00-1:00

RH 142

Steve Harris

Boundaries on Space-time

Th Oct 12

topology/ analysis

2:10-3:00

RH 202

Anneke Bart

Topological Groups acting on Hyperbolic Space

Th Oct 19

topology / geometry

12:00-1:00

RH 142

Steve Harris

Boundaries on Space-time

Th Oct 19

topology/ analysis

2:10-3:00

RH 202

Anneke Bart

Topological Groups acting on Hyperbolic Space

Tu Oct 24

algebra

3:10-4:00

RH 134

Greg Marks

Baer Rings and 2-Primal Rings (Cont'd)

Th Oct 26

topology / geometry

12:00-1:00

RH 142

Anneke Bart

(Immersed) Totally Geodesic Surfaces in Bianchi Groups.

Th Oct 26

topology/ analysis

2:10-3:00

RH 202

Bryan Clair

Topological Groups acting on Hyperbolic Space

Tu Oct 31

algebra

3:10-4:00

RH 134

Greg Marks

Baer Rings and 2-Primal Rings (Cont'd)

Th Nov 2

topology / geometry

12:00-1:00

RH 142

Steve Harris

Boundaries on Space-time

Th Nov 2

topology/ analysis

2:10-3:00

RH 202

Bryan Clair

Topological Groups acting on Hyperbolic Space

Tu Nov 7

algebra

3:10-4:00

RH 134

Greg Marks

Baer Rings and 2-Primal Rings (Cont'd)

Th Nov 9

topology / geometry

12:00-1:00

RH 142

Kevin Scannell

"(Super) Lie algebras and the space of all knots"

Th Nov 9

topology/ analysis

2:10-3:00

RH 202

Bryan Clair

Topological Groups acting on Hyperbolic Space