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Dualities, DT invariants and higher depth mock modular forms

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Speaker: 
Sergei Alexandrov
Affiliation: 
Laboratoire Charles Coulomb (CNRS), Montpellier
Date: 
Mon, 23/07/2018 - 14:00 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk
Using dualities of string theory, I derive modular constraints onthe generating function of MSW invariants, which coincide withgeneralized Donaldson-Thomas invariants of a Calabi-Yau threefoldat the large volume attractor point in the moduli space. Thefunction is labeled by a divisor and when the divisor isirreducible, it is known to be modular. I show that in the case ofa reducible divisor, the modularity is lost, but can be restored
in a non-holomorphic completion. I find a general form of thecompletion for arbitrary degree of reducibility and provide its explicit expression up to degree 5.
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