Informal Algebra and Geometry Seminar
Organizers: Sam DeHority, Junliang Shen.
Time: Friday 3:00- 4:30. Room: KT 801.
This is a seminar for talks/mini-lecture series on research topics related to algebraic geometry and related fields. The speakers are highly encouraged to go slowly and provide sufficient background and examples to make the talks friendly to non-experts and graduate students.
02.21 and 02.28. Title: Vertex algebras and moduli of Higgs bundles I/II
Speaker: Sam Dehority
Abstract: Motivated by a physics construction in 4d N=2 superconformal field theories, mathematicians have studied a class of vertex algebras with a number of interesting relations with the cohomology of moduli spaces of stable Higgs bundles of a curve C. We will discuss basic definitions and constructions in the theory of vertex algebras, and discuss examples, including Arakawa's construction of class S VOAs.
In the second lecture, we explain how characters of these vertex algebras often satisfy (quasi-)modular linear differential equations, with logarithmic terms in characters related to extensions of vertex algebra modules.
03.07. [No meeting due to the Lang Lecture].
(SPRING BREAK)
03.28. Title: Fourier-Mukai Transformations of certain upward flows
Speaker: David Fang
Abstract: Recently there was a paper of Hausel and Hitchin which developed the theory of upward flows/attracting loci in the moduli space of semistable Higgs bundles, and used them to for example to compute multiplicities of components of the global nilpotent cone. They also gave an incomplete picture of what the mirror of certain upward flows look like under some version of homological mirror symmetry. We give a more complete explanation of this mirror, using the duality theories for compactified Jacobians developed by Arinkin, Melo-Rapagnetta-Viviani, and Maulik-Shen-Yin.
04.04. [No meeting due to the GSP seminar]
04.11. [No meeting due to the GSP seminar]
04.18. Title: Vertex algebra and moduli of Higgs bundles III
Speaker: Sam DeHority
Abstract: After the spring break, Sam will continue to discuss the connection between VOA and the cohomology of the Hitchin moduli space.
05.02. Title: Vertex algebra and moduli of Higgs bundles IV
Speaker: Sam DeHority