Friday August 30, 2019 11:00 AM  12:00 AM Math Tower 5127
 Andrew Hanlon, Stony Brook University
An Overview of Homological Mirror SymmetryIn this talk, we will discuss some of the historical background and motivation for homological mirror symmetry. We will describe in minimal details the symplectic and algebraic objects involved in order to give a glimpse of where this seminar is headed.

Friday September 06, 2019 11:00 AM  12:00 AM Math Tower 5127
 Yuhan Sun, Stony Brook University
A first look at Lagrangian Floer theoryThis is an introductory talk to define the Lagrangian Floer (co)homology which comes from studying intersections of Lagrangian submanifolds and holomorphic disks. I will focus on examples to convey the ideas behind this topic. Technical details will only be presented by pictures. Prerequisites will be kept minimal.

Friday September 13, 2019 11:00 AM  12:00 AM Math Tower 5127
 Yi Wang, Stony Brook University
Product and higher operations in Lagrangian Floer theoryContinuing with Yuhan's talk, I will define the triangle product on the Floer complex, which descends to an associative product structure on cohomology. At chain level, however, the product is only associative up to homotopy given by higherorder operations. I will define all these operations by counting certain holomorphic disks whose boundaries connect Lagrangian intersection points, and explain how the limit configurations imply "Ainfinity" relations among the operations. Then we are ready to define the Fukaya category, modulo technical issues.

Friday September 20, 2019 11:00 AM  12:00 AM Math Tower 5127
 JinCheng Guu, Stony Brook University
Coherent SheavesWe will explain what coherent sheaves are, some of their cohomological properties, and sketch a proof for a reconstructing theorem: “good” schemes are determined by their derived category of coherent sheaves.

