Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.
Wednesday, December 5, 2018
11:10 a.m.
BA1170
PhD Candidate: Chia-Cheng Liu
Co-Supervisors: Joel Kamnitzer/Alexander Braverman
Thesis title: Semi-innite Cohomology, Quantum Group Cohomology, and the Kazhdan-Lusztig
Equivalence
The Kazhdan-Lusztig tensor equivalence is a monoidal functor which sends modules over ane
Lie algebras at a negative level to modules over quantum groups at a root of unity. A positive
level Kazhdan-Lusztig functor is dened using Arkhipov-Gaitsgory’s duality between ane Lie
algebras of positive and negative levels. We prove that the semi-innite cohomology functor
for positive level modules factors through the positive level Kazhdan-Lusztig functor and the
quantum group cohomology functor with respect to the positive part of Lusztig’s quantum
group. This is the main result of the thesis.
Monoidal structure of a category can be interpreted as factorization data on the associated
global category. We describe a conjectural reformulation of the Kazhdan-Lusztig tensor equivalence
in factorization terms. In this reformulation, the semi-innite cohomology functor at
positive level is naturally factorizable, and it is conjectured that the factorizable semi-innite
cohomology functor is essentially the positive level Kazhdan-Lusztig tensor functor modulo the
Riemann-Hilbert correspondence. Our main result provides an important technical tool in a
proposed approach to a proof of this conjecture.
A copy of the thesis can be found here: thesis_chiachengliu-1
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