Quantum Groups Seminar - Introduction to Quantized Enveloping Algebras and Advanced Topics

Explore the mathematical foundations and advanced concepts of quantum groups through this comprehensive seminar series from the Institute for Advanced Study. Begin with an introduction to quantized enveloping algebras and progress through the center of quantum groups, R-matrices, and braid group actions with PBW type basis constructions. Examine algebraic groups in characteristic p, quantum groups at roots of unity, and their representation theory. Conclude with an in-depth study of the Kazhdan-Lusztig category and equivalence, gaining insight into these fundamental structures that bridge quantum algebra, representation theory, and mathematical physics.

Syllabus

Introduction to quantized enveloping algebras - Leonardo Maltoni
Introduction to quantized enveloping algebras - Leonardo Maltoni
Center of quantum group - Arun Kannan
Center of quantum group pt2 - Arun Kannan
R-matrices - Elijah Bodish
R-matrices II - Elijah Bodish
Braid group actions and PBW type basis - Calder Morton-Ferguson
Braid group actions and PBW type basis pt2 - Calder Morton-Ferguson
Algebraic groups and all in characteristic p - Ivan Loseu
Quantum groups at roots of unity - Jay Taylor
Quantum groups at roots of unity - Jay Taylor
Representations of quantum groups at roots of 1 - Jize Yu
Representations of quantum groups at roots of 1 pt2- Jize Yu
Kazhdan-Lusztig category - Jin-Cheng Guu
Kazhdan-Lusztig category - Jin-Cheng Guu
Kazhdan-Lusztig equivalence - Pablo Boixeda Alvarez