
Bena Tshishiku
Mon Jan 8, 2018
4:00 pm
A basic problem in the study of fiber bundles is to compute the ring H*(BDiff(M)) of characteristic classes of bundles with fiber a smooth manifold M. When M is a surface, this problem has ties to algebraic topology, geometric group theory, and algebraic geometry. Currently, we know only a very small percentage of the total cohomology. In this...

Mon Dec 4, 2017
4:00 pm
Raphael Zentner (University of Regensburg): Irreducible SL(2,C)representations of integer homology 3spheres
We prove that the splicing of any two nontrivial knots in the 3sphere admits an irreducible SU(2)representation of its fundamental group. This uses instanton gauge theory, and in particular a nonvanishing result of KronheimerMrowka...

Sheel Ganatra
Tue Nov 28, 2017
4:00 pm
We introduce a new class of noncompact symplectic manifolds called
Liouville sectors and show they have wellbehaved, covariantly functorial
Fukaya categories. Stein manifolds frequently admit coverings by Liouville
sectors, which can be used to understand the Fukaya category of the total
space (we will study this geometry in examples). Our...

Nick Salter
Mon Nov 27, 2017
4:00 pm
This talk will be a discussion of some interesting and novel subgroups of the mapping class group that arise via algebrogeometric constructions. Our talk will focus on the special case of how the theory of plane algebraic curves (essentially just polynomials in two variables!) interacts with the mapping class group in subtle ways. The motivating...

Mon Nov 6, 2017
4:00 pm
Sheel Ganatra (USC): Liouville sectors and localizing Fukaya categories
We introduce a new class of Liouville manifoldswithboundary, called Liouville sectors, and show they have wellbehaved, covariantly functorial Fukaya/Floer theories. Stein manifolds frequently admit coverings by Liouville sectors, which can then be used to study the Fukaya...

YuShen Lin
Mon Oct 30, 2017
4:00 pm
We will start from the motivation of the tropical geometry. Then
we will explain how to use Lagrangian Floer theory to establish the
correspondence between the weighted counting of tropical curves to the
counting of holomorphic discs in K3 surfaces. In particular, the result
provides the existence of new holomorphic discs which do not...

Yi Ni
Mon Oct 9, 2017
4:00 pm
Prism manifolds are spherical 3manifolds with Dtype finite fundamental
groups. They can be parametrized by a pair of relatively prime integers p>1
and q. The realization problem of prism manifolds asks which prism manifolds
can be obtained by positive Dehn surgery on a knot in S^3. This problem has
been solved in the cases q<0 and q>p....