During his CAS Associate appointment, Professor Bradlow will co-organize one of the featured programs for Fall 2019 at the Mathematical Sciences Research Institute (MSRI) in Berkeley. Entitled Holomorphic Differentials in Mathematics and Physics, the program will bring together mathematicians and physicists with diverse backgrounds and perspectives but with a common interest in the central objects of the program.
Holomorphic differentials first appeared in late 19th-century mathematics. The simplest examples—differential 1-forms on a two-dimensional plane—are part of the basic machinery of calculus. More exotic versions of such differentials can be constructed on curved surfaces. After 150 years of study intricate links have been established between the resulting holomorphic differentials and geometric and analytic properties of the underlying surfaces. Participants in the MSRI program include experts on the role of holomorphic differentials in settings as diverse as geometric structures on surfaces (Teichmüller theory), the evolution of complex systems (dynamical systems), string theory and quantum field theory, and moduli spaces in algebraic geometry. Bradlow’s main interest has so far been in the relation between holomorphic differentials and moduli spaces of Higgs bundles. While at MSRI he plans to expand his research in directions championed by the other participants.