Tuesdays at 3:30pm-4:30pm in CH (Cockins Hall) 240 or as announced
Tuesday, October 13, 2009 |
| Speaker: Guido Mislin (Ohio State University) |
| Title: On the bounded cohomology of Lie Groups |
| Location: CH 240 |
| Time: 3:30pm |
Monday, November 9, 2009 |
| Speaker: Jonathan Bloom (Columbia University) |
| Title: Link surgery, monopole Floer homology, and odd Khovanov homology |
| Location: CH 240 |
| Time: 3:30pm |
| Abstract: I'll describe new invariants of a framed link in a 3-manifold, which
arise as the pages of a spectral sequence generalizing the surgery
exact triangle in monopole Floer homology. The construction introduces
a connection between the topology of link surgeries and the
combinatorics of polytopes called graph associahedra. For a classical
link L in S3, we obtain a sequence of bigraded vector spaces,
interpolating between the reduced, Z/2Z Khovanov homology of L and a
version of the monopole Floer homology of the branched double cover.
In addition, this perspective yields a simple, topological proof that
odd Khovanov homology is mutation invariant. I'll emphasize
low-dimensional topology through lots of pictures, and not the
technical details of Floer homology.
Paper reference: arxiv.org/abs/0903.3746, arxiv.org/abs/0909.0816 |
Tuesday, November 17, 2009 |
| Speaker: Matthew Day (Caltech) |
| Title: Mapping class groups of surfaces and nilpotent homogeneous spaces |
| Location: CH 240 |
| Time: 3:30pm |
| Abstract: The Morita homomorphisms are a series of homomorphisms defined on a series of subgroups of the mapping class group of a surface. Their definition involves a construction using the standard group homology chains of nilpotent quotients of the fundamental group of the surface. We introduce a procedure to turn the group homology chains of these nilpotent quotients into polynomial singular homology chains on the associated nilpotent homogeneous spaces (polynomial with respect to exponential coordinates). Using this procedure we get very nice extensions of the Morita homomorphisms to the entire mapping class group. |
Thursday, November 19, 2009 |
| Speaker: Andrew Putman (MIT) |
| Title: The Picard group of the moduli space of curves with level structures |
| Location: CH 240 |
| Time: 2:30pm |
| Abstract: The Picard group of an algebraic variety $X$ is the set of complex line bundles over $X$. In this talk, we will describe the Picard groups of certain finite covers of the moduli space of curves. The methods we use combine ideas from algebraic geometry, finite group theory, and algebraic/geometric topology. |
Tuesday, November 24, 2009 |
| Speaker: James Fowler (Ohio State University) |
| Title: TBA |
| Location: CH 240 |
| Time: 3:30pm |
| Abstract: TBA |