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Averaging to Higher Depth Mock Modular Forms

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BLHW01 - Number theory, machine learning and quantum black holes

In recent years, mock modular forms with depth higher than one have started to make their appearance in physics and mathematics, finding applications in diverse contexts such as black hole counting, geometric invariants, and two dimensional conformal field theories. Mathematically, one aspect of higher depth mock modular forms that distinguishes them from their depth one counterparts is the absence of well-established Eisenstein/Poincaré series representations for (pure) mock modular forms at depth one, which allows one to recognize pure mock modular forms as averages of simpler objects over SL2 . In this talk, we will discuss how a certain type of double Eisenstein series can give rise to a similar picture for higher depth mock modular forms and connections that this leads to for the holomorphic parts of mock modular forms.

This talk is part of the Isaac Newton Institute Seminar Series series.

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