June 3, 2020
TITLE: An update on hyperkahler metrics on moduli of Higgs bundles
ABSTRACT: In joint work with Davide Gaiotto and Greg Moore, we gave a new conjectural construction of the hyperkahler metric on moduli spaces of Higgs bundles, in which the key new ingredient was counts of BPS states (Donaldson-Thomas-type invariants).
Through the work of various authors, including me, Dumas, Fredrickson, Mazzeo, Swoboda, Weiss, Witt, there is now some evidence that this conjectural picture is correct. On the one hand, some of the asymptotic predictions which follow from the conjecture have been proven; on the other hand, there is numerical evidence that the conjecture is correct even far away from the asymptotic limit. I will review these developments.