Upcoming talk:
Date: Wednesday, April 2, 8-9 AM
Location: 双清C548
Speaker: Robert McRae, Tsinghua University
Title: Virasoro and triplet vertex algebras at positive rational central charge
Abstract: I will discuss ongoing joint work with Hao Li and Jinwei Yang on the structure of tensor categories of representations for the Virasoro Lie algebra at positive rational central charges c > 25, and their relations to the quantum group of sl_2 at roots of unity. As an application, we construct a triplet vertex algebra at any rational central charge c > 25 which contains the Virasoro vertex algebra of central charge c as a subalgebra and has automorphism group PSL(2,C). We expect that this triplet vertex algebra will have a non-semisimple modular tensor category of representations, and thus may be of interest for logarithmic conformal field theory.
Past Talks:
Date: Wednesday, March 5, 9-10 AM
Zoom Link: https://caltech.zoom.us/j/83185685455
Speaker: Lingfu Zhang (Caltech)
Title: Limiting Processes in the Theory of KPZ Universality
Abstract: A cornerstone of modern probability theory is the Central Limit Theorem, which states that the normal distribution (and, in a dynamic setting, Brownian motion) serves as the universal scaling limit for a broad class of random models, with numerous applications across science and engineering.
Over the past few decades, a new universality class—named after Kardar, Parisi, and Zhang (KPZ)—has emerged to describe another range of physical and probabilistic models, including growth processes, interacting particle systems, and random matrix models. While the analog of the Central Limit Theorem—the strong KPZ universality conjecture—remains open, key limiting processes, such as the KPZ fixed point and the directed landscape, have been constructed in recent years, with many properties (such as distribution functions) now understood. I will introduce these processes, and present recent progress (joint with Dauvergne) toward developing a unified limiting theory.
Date: Wednesday, November 27, 9-10 AM
Venue: Shuangqing C546
Zoom Link: https://caltech.zoom.us/j/83185685455
Speaker: Wenbin Yan, Tsinghua University
Title: 4d mirror symmetry for class-S theories
Abstract: We will discuss a 4d mirror symmetry for the class-S theories which relates the representation theory of the chiral quantization of the Higgs branch and the geometry of the Coulomb branch. We study the representation theory by using the 4d/VOA correspondence, Schur indices and modular differential equations, and match the data with the fixed manifolds of the Hitchin moduli spaces. This correspondence extends the connection between Higgs and Coulomb branch of Argyres-Douglas theories, and can provide systematic guidance for the study of the representation theory of vertex operator algebras by exploiting results from Hitchin systems.
Speaker: Yunqing Tang, Berkeley/Caltech
Title: The Arithmetic of Power Series and Applications to Period
Abstract: Borel and Dwork gave conditions on when a nice power series with rational number coefficients comes from a rational function in terms of meromorphic convergence radii at all places. Such a criterion was used in Dwork’s proof of the rationality of zeta functions of varieties over finite fields. Later, the work of André, Bost, Charles and many others generalized the rationality criterion of Dwork and deduced many applications in the arithmetic of differential equations and elliptic curves. In this talk, we will briefly review the history and then discuss some further refinements and generalizations of the criteria of André, Bost, and Charles and their application to irrationality of a special value of a certain Dirichlet L-function using rational approximations constructed by Zagier. This is joint work with Frank Calegari and Vesselin Dimitrov.
Date: Wednesday, October 30, 8 AM
Venue: Shuangqing C548 and online: https://caltech.zoom.us/j/83227207916?pwd=R8hqeEwfn7jb9ZVLt4px16a2LTAU00
Bio of Speaker: Yunqing Tang is a professor at Caltech and University of California, Berkeley specializing in number theory and arithmetic geometry. She received her PhD from Harvard University in 2016. Tang previously was a Member at the IAS, an Instructor at Princeton University, a junior researcher (Chargee de recherche) at CNRS/Universite Paris-Sud, and an assistant professor at Princeton University. Tang has recently been awarded a Sloan Research Fellowship, the SASTRA Ramanujan prize, and the AWM Microsoft Research Prize in Algebra and Number Theory.
Title: Khovanov homology for null homologous links in RP^3
Speaker: Daren Chen/陈大任, California Institute of Technology
Date: Wednesday March 6, 9 AM (Beijing Time)
Zoom Link: https://caltech.zoom.us/j/83185685455
Abstract:
Khovanov homology is a powerful invariant for studying links in S^3. Khovanov's originally definition is motivated by representation theory, and since then, there have been many interpretations of it from different perspectives. In this talk, we will review the interpretation given by Ozsvath and Szabo, relating it to the Heegaard Floer homology of the branched double cover of S^3 over the link, and explore how this allows an extension of the definition to null homologous links in the real projective space RP^3.
Title: Irregular conformal blocks and braiding properties
Speaker: Xia Gu, Tsinghua University
Time: Wednesday, December 6, 9:00 AM (Beijing Time)
Zoom Link: https://caltech.zoom.us/j/83185685455
Abstract:
In this talk, I would like to report our recent work arXiv: 2301.07957 & 2311.07960. We constructed the rank-1 irregular field in the free boson theory and computed the conformal blocks with one irregular field insertion using the integral representations. We obtained the monodromy and the braiding representations of these blocks by deforming the integral contours. Time permits, I will also talk about the relations of our results with the Stokes phenomena and the flat connection on conformal bundles.
