Madhusudhan Raman (Tata Institute for Fundamental Research, Mumbai)
Title: Chebyshev Wells, Automorphic Structures, and Resurgence
Abstract: We study the geometry and mechanics (both classical and quantum) of potential wells described by squares of Chebyshev polynomials. Classically, we show that these potentials can be put in a one-to-one correspondence with discrete subgroups of SL(2,R), and that its observables can be resummed into automorphic forms. Quantum mechanically, we show that in a small neighborhood of the locus cut out by them in the space of hyperelliptic curves, these systems exhibit low-orders/low-orders resurgence, where perturbative fluctuations about the vacuum determine perturbative fluctuations about nonperturbative saddles.