11 April 2016 to 15 July 2016
Institut Henri Poincaré
Europe/Paris timezone

Duncan

John Duncan, Emory University

Title: Optimal Mock Jacobi Forms

Abstract: Mock Jacobi forms were introduced by Dadholkar—Murthy—Zagier in order to count quantum degeneracies of single-centered black holes in string theory. They also appear naturally in umbral moonshine, where they encode dimensions of representations of certain finite groups. Call a mock Jacobi form optimal if its Fourier coefficients grow as slowly as possible. In this talk we review these notions, and present a classification, obtained in joint work with Miranda Cheng, of the optimal mock Jacobi forms of weight one that have integral Fourier coefficients. A positivity condition distinguishes the examples that are associated to Niemeier lattices by umbral moonshine.

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