报告题目：Tropical geometry, quantum affine algebras, and scattering amplitudes

报告人：李建荣 博士，兰州大学

时间：2023年4月7日（星期五）10:00-11:00

地点：东区第五教学楼5106教室

摘要：In this talk, I will talk about a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:

(1) We give a systematic construction of prime modules (including prime non-real modules) 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.

(3) We study limit g-vectors of cluster algebras. This is another way to obtain prime non-real modules of quantum affine algebras systematically. Using limit g-vectors, we construct new examples of non-real modules of quantum affine algebras.

This is joint work with Nick Early.

报告人简介

李建荣博士，从事量子仿射代数、丛代数和数学物理等方面的研究，曾在希伯来大学、威兹曼研究所、格拉兹大学等访问或做研究工作，曾主持和参与完成多项国家自然科学基金、海外基金，在JHEP、IMRN、Select Math.等国际著名期刊发表论文20余篇。