Academic Report of School of Mathematical Sciences [2025] No. 110

(Series Report for High-Level University Construction No. 1212)

Title: Structure constants of cohomology of Bott–Samelson variety with application to Schubert calculus

Speaker: Gui Tao (Peking University)

Time: 16:00-17:00, November 12, 2025 (Wednesday)

Location: Office Area 1420, Huiwen Building

Abstract:

The Bott–Samelson variety gives a resolution of singularities of the Schubert variety. We give an explicit, non-recursive, and type-uniform formula for all (equivariant) structure constants of the cohomology of Bott–Samelson varieties in arbitrary Lie types, using only the Cartan integers of the corresponding simple reflections in the word defining the Bott–Samelson variety. As an application, we derive an explicit, non-recursive, and type-uniform formula for all structure constants of (equivariant) Schubert calculus using the bridge building by Haibao Duan (and Matthieu Willems). In the Boolean case, this formula is (Graham) positive, which recovers Gao–Zhu’s recent formula on Boolean Schubert structure coefficients.

Speaker Profile:

Gui Tao is a postdoctoral researcher at the Beijing International Center for Mathematical Research, Peking University. He received his B.Sc. from the School of Mathematics, Sichuan University in 2018, and his Ph.D. from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2023, under the supervision of Researcher Xi Nanhua. His main research interests include Lie theory, representation theory, combinatorial algebraic geometry, and combinatorial Hodge theory.

All faculty and students are welcome!

Host: Ding Cong

School of Mathematical Sciences

November 5, 2025