Title: Studies of five-dimensional BPS spectra and applications to enumerative geometry
Abstract: The framework of spectral networks was introduced in physics as a way to compute BPS states of 4d N=2 gauge theories. In this talk I will review an extension of this framework, known as exponential networks, which arises in the study of 5d N=1 BPS states. Geometric engineering connects 5d N=1 BPS spectra to enumerative invariants of certain Calabi-Yau threefolds, I will review the computation of old and new results in the setting of local toric threefolds. I will also sketch a new perspective on this framework, which elucidates the geometric meaning of the invariants computed by networks, in terms of elementary data of A-branes in the mirror geometry, recovering an old conjecture of Joyce.
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