Past Seminars- Geometry and Topology

Printer-friendly version
  • 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 3-spheres We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka...
  • Sheel Ganatra
    Tue Nov 28, 2017
    4:00 pm
    We introduce a new class of non-compact symplectic manifolds called Liouville sectors and show they have well-behaved, 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 algebro-geometric 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 manifolds-with-boundary, called Liouville sectors, and show they have well-behaved, covariantly functorial Fukaya/Floer theories. Stein manifolds frequently admit coverings by Liouville sectors, which can then be used to study the Fukaya...
  • Yu-Shen 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 3-manifolds with D-type 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....