Geometry and Physics Seminar: Sara Filippini

We revisit the wall-crossing behaviour of solutions of a class of thermodynamic Bethe Ansatz type integral equations, expressed as sums of ''instanton corrections''. We explain how a set of tropical curves (with signs) emerges naturally from each instanton correction, then show that the weighted sum over all such curves is in fact a tropical count. This goes through to the q-deformed setting. This construction can be regarded as a formal mirror-symmetric statement in the framework proposed by Gaiotto, Moore and Neitzke. Joint work with J. Stoppa.