Colloquium: Partial Differential Equations and the Moduli Theory

Speaker: Yohsuke Imagi, ShanghaiTech University

Abstract: This talk will present an overview of the speaker's work. The goal of studying an equation would be to determine its solutions but the sense in which to determine them should depend upon the equation. Given, in particular, nonlinear PDEs (partial differential equations) one can generally not write down solutions; and even whether solutions exist or not is generally a difficult question. We may ask however whether moduli spaces (consisting of all solutions of given PDEs) have any interesting structures - which is given indeed some reasonable affirmative answers for some PDEs in geometry and string theory; but is still an open question for some higher-dimensional PDEs of the same kind, seemingly demanding an interaction between PDEs and such other objects as derived categories.