Tropical geometry, quantum affine algebras, and scattering amplitudes


报告时间:2023年10月10日:16:00 — 17:00


专家简介:李建荣,博士,维也纳大学研究员,主要从事表示论,特别是丛代数、量子群、组合数学以及在数学物理中的应用等方面的研究工作,相关研究工作发表于 Int. Math. Res. Not, Selecta Math., Math. Zeit. 等国际一流数学杂志。

报告摘要:In this talk, I will talk about a connection between tropical geometry,representations of quantum affine algebras, and scattering amplitudes in physics. (1) We give a systematic construction of prime modules (including prime non-realmodules) of quantum affine algebras using tropical geometry. We also introduce new objects which generalize positive tropical Grassmannians.(2) We propose a generalization of Grassmannian string integrals in physics, in which the integrand is a product indexed by prime modules of a quantum affine algebra.

We give a general formula of u-variables using prime tableaux (corresponding to prime modules of quantum affine algebras of type A) and Auslander-Reiten quivers of Grassmannian cluster categories.

This is joint work with Nick Early.