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SUMMARY:BPS modularity on Calabi-Yau threefolds - Boris Pioline (Sorbonne 
 Université)
DTSTART:20220826T101500Z
DTEND:20220826T111500Z
UID:TALK177260@talks.cam.ac.uk
DESCRIPTION:Unlike in cases with higher supersymmetry\, the spectrum of BP
 S states in type II string theory compactified on a Calabi-Yau threefold $
 X$ with generic $SU(3)$ holonomy remains partially understood. Mathematica
 lly\, the BPS indices coincide with the generalized Donaldson-Thomas invar
 iants associated to the derived category of coherent sheaves\, but they ar
 e rarely known explicitly. String dualities indicate that suitable generat
 ing series of rank 0 DT indices counting D4-D2-D0 bound states&nbsp\; shou
 ld transform as vector-valued mock modular forms\, in a very precise sense
 . I will spell out and test these predictions in the context of non-compac
 t threefolds of the form $X=K_S$ where $S$ is a Fano surface\, and for com
 pact Calabi-Yau threefolds with $b_2=1$ such as the quintic. Based on earl
 ier work with Sergey Alexandrov\, Sibasish Banerjee\, Nava Gaddam\, Jan Ma
 nschot\, and work in progress with Sergey Alexandrov\, Soheyla Feyzbakhsh\
 , Albrecht Klemm and Thorsten Schimannek.&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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