Academic Report of School of Mathematical Sciences [2026] No. 110

(Series Report for High-Level University Construction No. 1369)

Title：Lattice Bruhat intervals

Speaker：Postdoctoral Researcher Gui Tao (Westlake University)

Time：16:00-17:00, Nov. 4, 2026

Location：Room 1425, Huiwen Building, Yuehai Campus

Abstract:For a Bruhat interval $[x,y]$ in an arbitrary Coxeter group which is a lattice, we give a type-uniform construction of a convex polytope whose complete face lattice realizes $[x,y]$. This gives a polytopal realization of the coincidence between classical Kazhdan--Lusztig polynomials for lattice Bruhat intervals and Stanley's toric $g$-polynomials. For lattice Bruhat intervals in finite Weyl groups, we explain the relation with the toric geometry of Richardson varieties and derive formulas for their local and global intersection cohomology, as well as a Boolean criterion for rational smoothness. Joint with Yibo Gao (arXiv:2610.17798).

Speaker Profile：Gui Tao is a postdoctoral researcher at the Institute for Theoretical Sciences at Westlake University. He received his bachelor’s degree from the School of Mathematics at 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 primary research interests include Lie theory, representation theory, combinatorial algebraic geometry, and combinatorial Hodge theory.

Faculty and students are welcome to attend!

Invited by: Wan Jinkui

School of Mathematical Sciences

November 3, 2026