Geometry and Physics EMSW21-RTG

Northwestern University, Evanston IL

Investigators

Abstract

Abstract Award: DMS-0636646 Principal Investigator: Ezra Getzler, Boris Tsygan, Eric Zaslow Modern mathematical physics increasingly draws its techniques from a broad array of mathematical disciplines. Differential geometry plays a vital role in the study of quantum field theory through index theory, microlocal analysis, and mirror symmetry. Homotopy theory has become an essential tool in the study of geometry and physics, through the tools of A-infinity categories and derived categories. Representation theory and number theory have been developing links with conformal field theory through analogies between the Langlands program and the geometric Langlands program. Northwestern University is fortunate to have on its faculty world leaders in each of these directions of research. It is the ambition of this group to attain national leadership in training students and postdoctoral researchers in these fields. The physical world writes its laws in the language of mathematics, and progress in physics is intimately connected to progress in the development of mathematical methods and theories. In contemporary mathematical physics, geometry, in many different forms, and representation theory (the study of symmetry) play a central role. The mathematical physics group at Northwestern is particularly well-placed to attain its goal of increasing the number of US citizens who pursue careers in mathematical physics: the university attracts a particularly strong group of undergraduates (through its renowned Integrated Science Program, for example); the graduate program has become more selective; and the mathematics department has developed a postdoctoral program, which has been consistently successful at attracting women and has consistently placed postdocs in successful academic positions.