Tuesday September 11, 2018 5:30 PM  6:30 PM Math Tower 5127
 Samuel Grushevsky, Stony Brook University
An Introduction

Tuesday September 25, 2018 5:30 PM  6:30 PM Math Tower 5127
 Oleg Viro, Stony Brook University
Questions related to categorifications of quantum invariantsMost of the tools which Algebraic Topology provides for solutions of geometric problems are organized as functors from categories of geometric nature to algebraic categories. During the last 20 years this approach became mainstream also in Low Dimensional Topology. It was started with Khovanov's categorification which upgraded the Jones polynomial to homology. Since then many numerical and polynomial invariants have been categorified. Numerous categorifications used quite different approaches.
I date to propose an approach which is applicable to quantum invariants and seems to be the most natural. So far it is not clear to what extent it will really work. At least, I hope to ask good questions motivated by it. No preliminary knowledge assumed.

Tuesday October 16, 2018 5:30 PM  6:30 PM Math Tower 5127
 Dennis Sullivan, Stony Brook University
The idea of manifolds with singularitiesThese include algebraic varieties over C or R, analytic varieties over R or C and significantly the cycles and homologies in the socalled singular homology. Complex varieties give integral cycles of even dimension, while real varieties give mod two cycles. The singular definition of usual homology can be pictured by constructing a geometric realization of a singular chain, gluing the pieces together. To "compute" all of these things requires a general pictorial scheme which was provided by Thom and Whitney.

Tuesday November 20, 2018 5:30 PM  6:30 PM Math Tower P131
 Marcus Khuri, Stony Brook University
Topics in Mathematical Relativity

