Learning Seminar on Kazhdan-Lusztig theory

POSTECH Fall 2026

General Information: This is the webpage for the POSTECH Learning Seminar in representation theory from Fall 2026. The topic is Kazhdan-Lusztig theory.

Organizers: Valentin Buciumas, buciumas at postech dot ac dot kr.

Time and Place: Mondays 3:30pm-5:30pm in Room 404 (math building) unless otherwise noted.

Topic: Kazhdan-Lusztig theory. More precisely Hecke algebras, Kazhdan-Lusztig basis and polynomials, as well as generalizations and connections to (mostly) representation theory, geometry and combinatorics.

Syllabus: syllabus (somewhat vague at the moment, and subject to change)



Date Speaker Title Time and place References, notes etc.
September 7 Valentin Buciumas Introduction 3:30pm-5:30pm, Room 404
September 14 Tae Jun Park Coxeter Systems, the Bruhat Order, and the Iwahori-Hecke Algebra 3:30pm-5:30pm, Room 404 [3] ch. 1&2, [4] ch.2, [1] ch. 5&6
September 21 Tae Jun Park The Kazhdan-Lusztig Basis and Polynomials 3:30pm-5:30pm, Room 404 [3] ch. 3, [2], [1] ch. 7
September 28 Junhyuk Gu Category 𝒪 and the Kazhdan-Lusztig conjecture 3:30pm-5:30pm, Room 404 [3] ch. 3&13&14, [5] ch. 0&1
October 5 No talk: public holiday
October 12 Dowan Kwon Affine Weyl groups and affine KL theory 3:30pm-5:30pm, Room 404 [1] ch. 4.1-4.7, [6]
October 19 Valentin Buciumas Parabolic KL polynomials and Lusztig's conjecture(s) 3:30pm-5:30pm, Room 404 [10], [11]
October 26 Midterm week!
November 2 Jungtaek Hong KL theory for the spherical Hecke algebra 3:30pm-5:30pm, Room 404
November 9 Junhyuk Gu Soergel bimodules and category O 3:30pm-5:30pm, Room 404
November 16 Beida Xiao Flag Varieties, Schubert Varieties, and Their Singularities 3:30pm-5:30pm, Room 404
November 23 Beom-seok Kim Intersection Cohomology 3:30pm-5:30pm, Room 404
November 30 Jaeyong Ahn, Taeyung Lee KL polynomials, the combinatorial invariance theorem and the hypercube decomposition theorem 3:30pm-5:30pm, Room 404 [7], [8], [9]
December 7 Zheming Xu Quantum affine algebras and Nakajima quiver varieties (topic might change) 3:30pm-5:30pm, Room 404
December 14 TBA OpenAI's proof of the combinatorial invariance theorem 3:30pm-5:30pm, Room 404 [12]
December 21 Finals week!

References:
[1] Humphreys: Reflection groups and Coxeter groups
[2] Kazhdan-Lusztig: Representations of Coxeter Groups and Hecke Algebras
[3] Elias-Makisumi-Thiel-Williamson: Introduction to Soergel bimodules
[4] Bjorner-Brenti: Combinatorics of Coxeter groups
[5] Humphreys: Representations of semisimple Lie Algebras in the BGG category O
[6] Nelsen-Ram: Kostka-Foulkes polynomials and Macdonald spherical functions
[7] Williamson et al.: Towards combinatorial invariance for Kazhdan-Lusztig polynomials
[8] Williamson et al.: Advancing mathematics by guiding human intuition with AI
[9] Brenti: Kazhdan-Lusztig polynomials: history, problems, and combinatorial invariance
[10] Soergel: Kazhdan-Lusztig polynomials and a combinatoric[s] for tilting modules.
[11] Jantzen: Representations of Algebraic Groups
[12] OpenAI: Combinatorial invariance of Kazhdan-Lusztig polynomials, available here