SGGTC seminars this week
Robert Lipshitz
We have two fairly different SGGTC talks this week, and the GT and AG seminars are also SGGTC-related:
Friday, April 13, 9:30 a.m., Math 520:
Igor Kriz, "Field theories, homotopy realizations and Khovanov homology"
Abstract: I will talk about joint work with Po Hu and Daniel Kriz on realizations of 1+1-field theories valued in categories in modules over rigid ring spectra in stable homotopy theory. As an application, I will discuss an alternate approach to a recent result of Robert Lipshitz and Sucharit Sarkar constructing a stable homotopy refinement of Khovanov homology, and some related topics.
Friday, April 13, 10:45 a.m., Math 520:
Eduardo Gonzalez, "Seidel Elements and Mirror Transformations"
Abstract: Let X be a non-singular projective toric variety whose anti-canonical class is semipositive (nef). I will present work with Hiroshi Iritani regarding the relation of Givental's mirror symmetry transformations with Seidel's invertible elements in the Quantum Cohomology of X. If time permits I will describe a conjecture due to Chan-Lau-Leung-Tseng that relate this work to lagrangian Floer theory superpotentials introduced by Fukaya-Ohta-Ono-Oh.
Friday, April 13, 1:15 p.m., Math 520:
Ina Petkova “On the gradings and decategorification of Bordered Heegaard Floer homology”
Abstract: Bordered Heegaard Floer homology is a Floer theory over Z/2 for manifolds with boundary. After gluing, it recovers Heegaard Floer homology for closed manifolds. I will describe the bordered Floer package and some applications to knot theory. Then I will define a Z/2 differential grading, and discuss the decategorification of bordered Heegaard Floer homology with this grading.
Friday, April 13, 2:00 p.m., Math 520:
Constantin Teleman, "Gauge theory, mirror symmetry and Langlands duality"
Abstract: The work of Kapustin and Witten has confirmed the importance of Langlands duality in 4-dimensional gauge theory. Less known is the appearance of Langlands duality in 2-dimensional gauge theory (the one that relates to volumes of moduli of flat connections and Verlinde formulas). In this talk, I will spell out the appearance of this duality in relation to mirror symmetry, specifically in describing the mirror to gauged Gromov-Witten theory. This relates to older work of Donaldson and Hitchin on monopoles, of Seiberg and Witten on 3d gauge theory, and a beautiful description of the homology of the loop Grassmannian due to Bezrukavnikov-Finkelberg-Mirkovic. At a very impressionistic level, the talk will be accessible to people with no prior exposure to some of these notions.
I'll be at at least the first three; we'll head to lunch after the second talk. I look forward to seeing you there!
Robert