The Physics of Modularity

Modularity is at the heart of many deep results in mathematics--from the proof of Fermat’s last theorem to moonshine to the Langlands correspondence. At the same time, modular group representations and automorphic forms underlie many interesting physical phenomena in quantum field theory and string theory, including understanding of dualities, boundary conditions, and supersymmetric black holes, among other things. This conference will bring together physicists and mathematicians to discuss emerging connections between a web of fundamental objects in physics and mathematics, united in the crucial role played by modularity.

Topics: new moonshines and mock modular forms; vertex operator algebras arising in supersymmetric gauge theories; topological invariants of 3- and 4-manifolds; topological QFTs and topological phases in condensed matter physics; topological string theory, Donaldson-Thomas theory, and enumerative geometry; scattering amplitudes in string theory; 2d conformal field theories, the modular bootstrap, and connections to 3d quantum gravity