Vignettes in Physical Mathematics - Natalie Paquette - Joseph Henry Room

Tue, Feb 5, 2019, 2:30 pm
Joseph Henry Room, Jadwin Hall

Abstract: Fundamental physics generates new mathematics. String theory and quantum field theory leverage exact and infrared dualities to provide equivalent descriptions of physical objects, some of which admit rigorous definitions; dual pairs of objects are sometimes even formalized using two a priori distinct areas of mathematics. Conversely, deep ideas in modern mathematics have been brought to bear on physical questions, yielding beautiful and unexpected results. `Physical mathematics' is the moniker sometimes given to the field which generates this cross-departmental exchange of techniques and results. I will describe new advances emerging from physical mathematics on two complementary fronts: 1.) new symmetries of supersymmetric string vacua motivated by the mathematical subject of moonshine and 2.) the action of duality on boundary conditions in (2+1)d quantum field theories, and some of its applications to geometry.