Speaker: 李鹏辉，清华大学丘成桐数学科学中心

Inviter: 聂思安

Title: Coxeter gluing in Betti Langlands

Language: Chinese

Time & Venue: 2026.09.18 10:30-11:30 南楼N820

Abstract: A well-known fact states that every Coxeter group can be glued (via colimits) from its finite Coxeter subgroups. We propose an analogous construction for the automorphic category in the Betti Langlands program: given a family of smooth curves degenerating to a nodal curve, we define a Coxeter gluing functor from the automorphic category of the smooth curve to a limit of automorphic categories on the nodal curve. This limit is indexed by twisting types, paralleling the Coxeter group case. We conjecture that the Coxeter gluing functor is an equivalence, and show that the conjecture holds if and only if the automorphic gluing conjecture of Nadler–Yun holds. We prove the Coxeter gluing conjecture for genus-one families. This is a joint work in progress with David Nadler and Zhiwei Yun.