Three Avatars of Mock Modularity

Abstract

Mock theta functions were introduced by Ramanujan in 1920 but a proper understanding of mock modularity has emerged only recently with the work of Zwegers in 2002. In these lectures we describe three manifestations of this apparently exotic mathematics in three important physical contexts of holography, topology and duality where mock modularity has come to play an important role.

arXiv comment36 pages. Lectures delivered at 2020 ICTP Online Summer School on String Theory and Related Topics. Based on arXiv:1208.4074, arXiv:1905.05207, arXiv:2004.14387

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