Title: From divergence to convergence
Speaker: Ovidiu Costin
Abstract: Asymptotic expansions play a major role in our understanding of difficult mathematical problems. As it turns out however, most often these expansions do not converge --at least not in any classical sense. In the last few decades, through the effort of many mathematicians, methods to remedy these divergences have emerged in substantial generality. Resummation techniques are now used to solve previously intractable problems in analysis, nonlinear PDEs and mathematical physics. In physics their application led to major progress in our understanding of mathematical geodesy, interaction of matter with intense laser fields, realistic models of String Theory, Quantum Chromodynamics, modularity and Ramanujan Mock Theta functions and many more.
I will focus on the fundamental ideas behind resummation of divergent expansions, on their applications, and on what lies ahead.”