Geometry Seminar
Spaces of positive scalar curvature metrics on nonorientable manifolds
Speaker: Milan Zerbin (U. Augsburg)Date: Wednesday, 30 April 2025 - 12:00Place: Aula Naranja, ICMAT
Abstract:
Programme:
Joyce Structures on Moduli of Meromorphic Quadratic Differentials
Speaker: Menelaos Zikidis (U. Sheffield)
Time: 10:30
Abstract: Joyce Structures are the output of Bridgeland's largely conjectural programme aiming to encode the Donaldson-Thomas 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 this case the space of stability conditions becomes the moduli of meromorphic quadratic differentials on wild algebraic curves and Joyce structures arise as Ehresmann 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.
Coffee break: 11:30 - 12:00
Spaces of positive scalar curvature metrics on nonorientable manifolds
Milan Zerbin (U. Augsburg)
Time: 12:00
Abstract: The question, which manifolds admit a metric of everywhere positive scalar curvature has sparked much interest in the last decades. With the surgery results of Gromov--Lawson and Schoen--Yau and their later refinements, one can use techniques from differential and algebraic topology (such as bordism theory) to arrive at partial answers. One such technique was employed by Ebert and Wiemeler in 2022 to characterize the homotopy type of the space of positive scalar curvature metrics on spin manifolds. We extend their result to nonorientable manifolds of dimension bigger than 10.
