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Ramanujan’s influence on string theory, black holes and moonshine. (English) Zbl 1462.81157

Summary: 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81-03 History of quantum theory
83-03 History of relativity and gravitational theory
11-03 History of number theory
01A70 Biographies, obituaries, personalia, bibliographies
11F22 Relationship to Lie algebras and finite simple groups
11F37 Forms of half-integer weight; nonholomorphic modular forms
20D08 Simple groups: sporadic groups
83C57 Black holes

Biographic References:

Ramanujan, Srinivasa
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References:

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