Number Theory Seminar

Since its introduction in 1987, the incredibly beautiful geometry of Hitchin fibrations have had deep impact on many branches of mathematics, from mathematical physics, symplectic geometry, to geometric representation theory, number theory, and so on. In recent years, there has been a lot of progress towards understanding its non-linear analogues, which have seen applications in relative trace formulas. I will discuss some recent progress in stability of generalized Higgs bundles, and its motivation from number theory. The talk is based on joint work in progress with Andres Fernandez Herrero and Siqing Zhang, and will focus more on the big picture and be accessible.