Ramanujan's influence on string theory, black holes and moonshine

TL;DR

This paper explores Ramanujan's mathematical contributions, especially q-series and modular forms, and their significant influence on modern physics topics like string theory, black holes, and moonshine phenomena.

Contribution

It provides an overview of Ramanujan's work's impact on physics, including recent developments in black hole entropy and AdS/CFT correspondence.

Findings

Ramanujan's work on modular forms influences string theory and black hole physics.

Connections between moonshine phenomena and conformal field theories are highlighted.

Recent advances link Ramanujan's mathematics to black hole entropy calculations.

Abstract

Ramanujan influenced many areas of mathematics, but his work on q-series, on the growth of coefficients of modular forms, and on mock modular forms stands out for its depth and breadth of applications. I will give a brief overview of how this part of Ramanujan's work has influenced physics with an emphasis on applications to string theory, counting of black hole states and moonshine. This paper contains the material from my presentation at the meeting celebrating the centenary of Ramanujan's election as FRS and adds some additional material on black hole entropy and the AdS/CFT correspondence.