This series consists of talks in the area of Mathematical Physics.
I will review the relation between the A twist of 3d N=4 gauge theories and
the conformal blocks/chiral cohomology of 2d chiral algebras.
This talk will cover my interpretation of Teleman's article "Gauge theory and mirror symmetry."
Connections between representation categories of quantum groups and vertex operator algebras (VOAs) have been studied since the 1990s starting with the pioneering work of Kazhdan and Lusztig. Recently, connections have been found between unrolled quantum groups and certain families of VOAs. In this talk, I will introduce unrolled quantum groups and describe their connections to the Singlet, Triplet, and Bp vertex operator algebras.
Factorization algebras provide a flexible language for describing the observables of a perturbative QFT, as shown in joint work with Kevin Costello. In joint work with Eugene Rabinovich and Brian Williams, we extend those constructions to a manifold with boundary for a special class of theories that includes, as an example, a perturbative version of the correspondence between chiral U(1) currents on a Riemann surface and abelian Chern-Simons theory on a bulk 3-manifold.
Absolute Gromov-Witten theory is known to have many nice structural properties, such as quantum cohomology, WDVV equation, Givental's formalism, mirror theorem, CohFT etc.. In this talk, I will explain how to obtain parallel structures for relative Gromov-Witten theory via the relation between relative and orbifold Gromov-Witten invariants. This is based on joint works with Honglu Fan, Hsian-Hua Tseng and Longting Wu.