The study of BPS states in string theory and supersymmetric gauge theories prompted the development of new mathematical tools to analyze geometric properties of manifolds of various dimensions. In this talk I will introduce the framework of exponential networks, a novel approach to computing various types of enumerative invariants of toric CalabiYau threefolds from the geometry of Riemann surfaces. The structure behind this framework hinges on wallcrossing phenomena involving different kinds of BPS spectra, described by a synthesis of the wallcrossing formulae of CecottiVafa and KontsevichSoibelman inspired by work of GaiottoMooreNeitzke. While providing an effective way to study DonaldsonThomas invariants, an interesting byproduct of exponential networks is the prediction of unexpected relations between the latter and new `3d5d' invariants, as well as (for specific geometries) knot invariants.
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BPS States and Geometry
Research Group:
Pietro Longhi
Schedule:
Wednesday, October 7, 2020  16:00
Location:
Online
Abstract:
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