The Conformal Bootstrap and Mathematics

The conformal bootstrap is a method originating in physics that seeks to define and study conformal quantum field theories in two and higher dimensions. In recent years, surprising connections have emerged between the conformal bootstrap and several areas of mathematics, including the spectral theory of automorphic forms, the sphere packing problem, and related questions in geometry, analysis, and number theory. These developments suggest both that the conformal bootstrap “knows” a remarkable amount of mathematics, and that these mathematical structures can offer new ways of understanding quantum field theory.

This workshop will bring together experts from conformal field theory, number theory, spectral geometry, discrete geometry, and related fields to explore these emerging connections. One goal is to investigate how ideas and techniques from the conformal bootstrap can lead to new advances in mathematics. A complementary goal is to use insights from these mathematical disciplines to sharpen our understanding of conformal field theory and quantum field theory more broadly.

Organizers: James Bonifacio, University of Mississippi; Henry Cohn, MIT; Dalimil Mazáč, Institute of Theoretical Physics, Saclay; and Peter Sarnak, IAS