Quantum Difference Equations, Shuffle Algebras and Maulik-Okounkov Quantum Affine Algebras

Speaker: Tianqing Zhu (YMSC, Tsinghua University)

Host: Yehao Zhou

Time:
Lecture 1: 10:00 am~11:30 am, Monday, March 10
Lecture 2: 10:00 am~11:30 am, Wednesday, March 12
Lecture 3: 10:00 am~11:30 am, Friday, March 15
Lecture 4: 10:00 am~11:30 am, Monday, March 17
Lecture 5: 10:00 am~11:30 am, Wednesday, March 19
Lecture 6: 10:00 am~11:30 am, Friday, March 21

Location: Room 1110 at SIMIS

Abstract: This is a series of talk on explaining the connections between the Maulik-Okounkov quantum affine algebras and shuffle algebras via the methods of difference equations in representation theory and enumerative geometry. I will explain the following topics during the talks:

1. K-theoretic stable envelopes and Maulik-Okounkov quantum affine algebras.
2. Quantum difference equations from quasimap countings.
3. Shuffle algebras of affine type A and slope factorisations
4. Algebraic quantum difference equations from shuffle algebras of affine type A.
5. Proof of the isomorphism between shuffle algebras and MO quantum affine algebras.
6. Applications to solving the qKZ equation in the representation theory.