Abstract：Hitchin’s integrable systems lie in the crossroads of geometry, representation theory, and mathematical physics. I will discuss two central conjectures raised in the last two decades which greatly influenced the development for the algebraic geometry of Hitchin moduli spaces. The first is the P=W conjecture, which concerns the interaction of the topology of the Hitchin system and the non-abelian Hodge correspondence. The second is the topological mirror symmetry conjecture which connects the Langlands duality of groups and the mirror symmetry for Hitchin systems. I will explain that both conjectures can be proved in a uniform way, via vanishing cycles techniques and support theorem. Based on joint work with Davesh Maulik.

Speaker Profile: Junliang Shen joins Yale as a research scientist in the Department of Mathematics, and will be appointed as an Assistant Professor. His research area is algebraic geometry, particularly the study of moduli spaces. He is interested in using tools from algebraic geometry to solve questions and conjectures rooted in topology, geometry, and mathematical physics.  He was awarded the SwissMAP Innovator Prize in 2018. Junliang obtained his B.S. from Peking University, and his Ph.D. in mathematics from ETH Zurich. Prior to arriving at Yale, he worked as a C. L. E. Moore instructor at MIT. 

Seminar （2）：

Abstract：We present an effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].

Speaker Profile: Si Li received his PhD in Mathematics from Harvard University in 2011. Subsequently, he was an Assistant Professor at Boas, Northwestern University, an Assistant Professor at Boston University and a Visiting Associate Scientist at the University of Tokyo. He is currently a Professor in the Department of Mathematics at Tsinghua University. He was awarded the Morningside Mathematics Prize Gold Medal at the World Congress of Chinese Mathematicians in 2016.