应兰州大学数学与统计学院邀请，维也纳大学研究员李建荣将于2026年4月19-22日期间访问兰州大学，期间举办专题学术报告，欢迎全校师生参加。

报告题目一：Boundary q-characters of finite dimensional representations of quantum affine symmetric pairs

报告时间：2026年4月22日(星期三)上午9:30

报告地点：理工楼631

报告摘要：Frenkel and Reshetikhin introduced q-characters for finite-dimensional representations of quantum affine algebras, providing a fundamental tool in their representation theory. Together with Tomasz Przezdziecki, we defined boundary q-characters for finite dimensional representations of quantum affine symmetric pairs of split and quasi-split types. In this talk, I will present a new joint work Tomasz Przezdziecki on evaluation modules for split quantum affine symmetric pairs. By computing the action of generators in Lu and Wang’s Drinfeld-type presentation on Gelfand–Tsetlin bases, we determine the spectrum of a large commutative subalgebra arising from this presentation. This leads to an explicit formula for boundary analogues of q-characters, which we interpret combinatorially in terms of semistandard Young tableaux. Our results show that boundary q-characters share familiar features with ordinary q-characters, while also exhibiting new phenomena, including an additional symmetry.

报告题目二：Tropical symmetries of cluster algebras

报告时间：2026年4月22日(星期三)上午10:30

报告地点：理工楼631

报告摘要：In this talk, I will present joint work with James Drummond and Ömer Gürdoğan on tropicalizations of quasi-automorphisms of cluster algebras. We study tropicalizations of quasi-automorphisms of cluster algebras and show that their induced action on g-vectors can be realized by tropicalizing their action on the homogeneous X-variables (\hat{y}-variables) of a chosen initial cluster. This perspective allows us to interpret the action on g-vectors as a change of coordinates in the tropical setting. Focusing on Grassmannian cluster algebras, we analyze tropicalizations of quasi-automorphisms in detail. In particular, we derive tropical analogues of the braid group action and the twist map, both on g-vectors and on tableaux. We also introduce the notions of unstable and stable fixed points for quasi-automorphisms. As an application, we show that the number of prime non-real tableaux with a fixed number of columns in SSYT(3, [9]) and SSYT(4, [8]), arising from the braid group action on stable fixed points, is governed by Euler’s totient function. Furthermore, we apply our results to scattering amplitudes in physics, providing a new interpretation of the square root appearing in the four-mass box integral in terms of stable fixed points of quasi-automorphisms of the Grassmannian cluster algebra C[Gr(4, 8)].

报告人简介

李建荣，现为维也纳大学研究员，从事量子群，表示论，丛代数，数学物理研究，完成国家自然科学基金青年基金项目一项，在 Selecta Mathematica,Mathematische Zeitschrift, Int. Math. Res. Notices, J. Algebra, Algeb. Rep. Theory, J. Algebraic Comb, J. Lie theory 等国际SCI期刊上发表学术论文30余篇。

甘肃省计算数学基础学科研究中心

数学与统计学院

萃英学院

2026年4月20日