ABSTRACT: Over ten years ago, Chiodo and Ruan proved a genus-zero global mirror theorem, relating the Gromov-Witten invariants of the quintic threefold to the corresponding Fan-Jarvis-Ruan-Witten invariants. Moreover, they suggested that the genus-zero relationship quantizes to an all-genus statement. In this talk, I’ll describe recent work with Huai-liang Chang, Shuai Guo, and Jun Li to compute higher-genus FJRW invariants and … Read More
ABSTRACT: I will explain a toy and ad hoc instance of mirror symmetry which relates compact Fukaya categories of certain simple plumbings of 3-spheres to derived categories arising from pairs of floppable curves in 3-folds. The appropriate big picture is largely absent. This talk reports on joint work in regress with Jonny Evans and Michael Wemyss.
ABSTRACT: How many faces in each dimension can a simplicial polytope have? This question turns out to have a beautiful answer, which was conjectured by McMullen in 1971 and proved by Stanley and Billera-Lee in the 80s. It is natural to ask what one can say for other combinatorial structures. I will review several instances where hard Lefschetz provides the … Read More
ABSTRACT: In this talk, I will discuss an ongoing joint project with Zhengyu Zong on the Gromov-Witten/Donaldson-Thomas correspondence for local gerby curves, as an orbifold generalization of the corresponding work on the smooth case by Bryan-Pandharipande and Okounkov-Pandharipande. By applying degeneration formulas, the correspondence can be reduced to the case of [C^2/Z_{n+1}] \times P^1, where the 3-point relative GW/DT invariants … Read More
ABSTRACT: I will discuss the change of quantum cohomology of toric stacks under flips.
ABSTRACT: On February 5, I discussed the problem of understanding the representation theory of Hecke correspondences between moduli spaces of stable sheaves on a smooth projective surface S (and presented reasons why one would care, stemming from mathematical physics and algebraic geometry). In this talk, I will give details on the proof, by studying the geometry and intesection theory of … Read More
ABSTRACT: I will describe recent results and conjectures relating knot invariants (such as HOMFLY-PT polynomial and Khovanov-Rozansky homology) to algebraic geometry of the Hilbert scheme of points on the plane. The talk is based on joint works with Andrei Negut, Jacob Rasmussen and Matthew Hogancamp.
ABSTRACT: I will introduce the concept of monoidal gerbes and show how to use them to twist suitable monoidal tensor categories. We will see interesting examples of this construction related to moduli stacks of objects in Calabi-Yau categories. For 3-Calabi-Yau categories we can go even further by constructing interesting monoidal functors. This allows us to define the Cohomological Hall (co)Algebra.