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BPS States and Geometry

Pietro Longhi
Wednesday, October 7, 2020 - 16:00

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 Calabi-Yau threefolds from the geometry of Riemann surfaces. The structure behind this framework hinges on wall-crossing phenomena involving different kinds of BPS spectra, described by a synthesis of the wall-crossing formulae of Cecotti-Vafa and Kontsevich-Soibelman inspired by work of Gaiotto-Moore-Neitzke. While providing an effective way to study Donaldson-Thomas invariants, an interesting byproduct of exponential networks is the prediction of unexpected relations between the latter and new `3d-5d' invariants, as well as (for specific geometries) knot invariants.

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