|
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 |