Denis Nesterov: Enumerative mirror symmetry for moduli spaces of Higgs bundles

Abstract

We will discuss a (conjectural) relation between curve-counting invariants of moduli spaces of Higgs SL-bundles and PGL-bundles, which are dual spaces in the sense of Mirror symmetry. In a nutshell, certain invariants associated to these moduli spaces are equal up to a simple transformation. Such relation is an instance of Mirror symmetry, which contrasts with the case of Calabi–Yau threefolds, for which curve-counting invariants of one threefold are exchanged with periods of its dual. We will also present explicit conjectural formulas for the invariants in question, as well as theoretical and computational evidences for the relation.