Number Theory and Representation Theory

Research Group

Introduction

For number theory, we focus on
- Additive combinatorics (A. Best): Furstenberg-Sárközy and Szemerédi type theorems.
- Arithmetic of $L$-functions: (W. He, E. Lecouturier, D. Yan, X. Yan, X. Zhu): Arithmetic statistics of Selmer groups, Iwasawa theory, BSD conjecture, Eisenstein congruences.
- Analytic methods for $L$-functions and automorphic forms (C. Lupu, W. Wang, D. Wu): Multi zeta and $L$-functions, mixed polyharmonic automorphic forms, Riemann hypothesis.
- $p$-adic geometry (T-A. Azzouz, Y-S. Moon, K. Shimizu): Families of $p$-adic Galois representations, $p$-adic Hodge theory, $p$-adic cohomologies, $p$-adic differential equations.
- Automorphic forms (T. Deng): Stability results for Langlands Shahidi Gamma factors, Arthur packets for (quasi-plit) classical groups over R, Eisenstein cohomology.
For representation theory, we focus on triangulated categories, quiver representations, cluster theory, Lie theory, quantum groups, etc. While emphasising algebraic side of the theory, we also explore its connection to geometry, topology and mahematical physics, e.g. stability conditions, mapping class groups, mirror symmetry and string theory.