Menelaos Zikidis (University of Pittsburgh): Joyce Structures on Moduli of Quadratic Differentials

Abstract: Joyce Structures are the output of Bridgeland’s largely conjectural program aiming to encode the DT- invariants of triangulated CY3 categories in a geometric structure over their space of stability conditions, akin to Frobenius structures in GW-theory. In this talk I will concentrate on the main class of examples we can currently construct a Joyce structure, namely on certain categories associated to quivers with potential. In those cases, the space of stability conditions becomes the moduli of meromorphic quadratic differentials on wild algebraic curves and Joyce structures arise as isomonodromy connections on a space parametrising irregular parabolic Higgs bundles and flat connections, a model resembling a complexification of the Hitchin system. These structures naturally give rise to a class of complex Hyperkähler manifolds and admit a twistor space description.