Algebra-Topology Seminar
We meet on Mondays, 12:15 pm in HG G 43. If you have any questions send an email to one of the organizers.
Spring Semester 2012
| Date |
Speaker |
Title |
Time |
Location |
| 27-feb-2012 (mon) |
Soren Galatius
|
Stable cohomology of moduli spaces of high dimensional manifolds
|
12:15-13:15 |
HG G 43 |
| Abstract: |
In recent work with Randal-Williams (arXiv:1201.3527v1), we study the space of all possible compact submanifolds of euclidean space with prescribed boundary P. I will start by defining this space properly and explain how its cohomology gives characteristic classes of manifold bundles with prescribed boundary. The monoid of self-bordisms of P acts on this cohomology, and the invariants give characteristic classes of manifold bundles which are unchanged by fiber gluing with trivial manifold bundles (similarly to how Pontryagin or Chern classes of vector bundles are unchanged by fiberwise summing with trivial vector bundles). Then I will explain our main theorem, which determines this ring of invariants in the case where P has odd dimension (2n-1) and the bounding manifolds are required to be (n-1)-connected relative to P. The case where P is the circle is essentially the Madsen--Weiss theorem about stable cohomology of moduli space of Riemann surfaces. The case where P is a (2n-1)-sphere is a higher-dimensional analogue of Madsen--Weiss, concerning the connected sum of g copies of S^n times S^n. |
| Speakers: |
Soren Galatius
(Stanford University)
|
|
| 19-mar-2012 (mon) |
Olivier Schiffmann
|
The Hall algebra of Spec(Z)
|
12:15-13:15 |
HG G 43 |
| Abstract: |
Hall algebras of abelian categories of representations of quivers over finite fields are known, since the work of Ringel, to produce Drinfeld-Jimbo quantum groups. Hall algebras of abelian categories of coherent sheaves on smooth projective curve over finite fields are known, since the work of Kapranov, to produce interesting infinite dimensional quantum groups. In this talk,we will try to make sense of the Hall algebra of the category of vector bundles over (a suitable compactification of) Spec(\mathbb{Z}), and relate it to some kind of shuffle algebra.
Based on joint work with M. Kapranov and E. Vasserot.
|
| Speakers: |
Olivier Schiffmann
(Institut de Mathématiques de Jussieu, Paris)
|
|
| 26-mar-2012 (mon) |
Cristina Pagliantini
|
Relative (continuous) bounded cohomology
|
12:15-13:15 |
HG G 43 |
| Abstract: |
The understanding of bounded cohomology of a space is mostly based on the relationship between bounded cohomology of spaces and of groups established by Gromov, Ivanov (and by Monod in the case of continuous cohomology). In the relative context, starting from a definition of bounded cohomology of pairs of groups due to Gromov, we provide an extension of Gromov's, Ivanov's and Monod's results for pairs of topological spaces. This is joint work with Roberto Frigerio. |
| Speakers: |
Cristina Pagliantini
(Università di Pisa)
|
|
| 2-apr-2012 (mon) |
Giovanni Gandini
|
Finiteness properties of lattices in automorphism groups of CAT(0) complexes
|
12:15-13:15 |
HG G 43 |
| Speakers: |
Giovanni Gandini
(University of Southampton, UK)
|
|
| 9-apr-2012 (mon) |
|
Eastern break
|
|
HG G 43 |
|
|
| 16-apr-2012 (mon) |
|
Sechseläuten
|
|
HG G 43 |
|
|
| 30-apr-2012 (mon) |
Armin Shalile
|
On the center of Brauer algebras and modular character theory
|
12:15-13:15 |
HG G 43 |
| Abstract: |
We define Brauer characters for Brauer algebras which share many of the features of Brauer characters defined for finite groups. Since notions such as conjugacy classes and orders of elements are not a priori meaningful for Brauer algebras, we show which structure replaces the conjugacy classes and determine eigenvalues associated to these. Furthermore, we will show how this approach can be used to determine the center of the Brauer algebra. |
| Speakers: |
Armin Shalile
(Universität Stuttgart)
|
|
