Deformations of Cusp Singularities of Algebraic Surfaces and Mirror Symmetry

Explore a comprehensive lecture on the deformations of cusp singularities in algebraic surfaces and their connection to mirror symmetry. Delve into the emergence of cusp singularities on degenerate surfaces at the boundary of the functorial compactification of the moduli space for surfaces of general type. Examine the Milnor fiber of a smoothing of a cusp singularity and its mirror relationship to log Calabi-Yau surfaces. Investigate the conjectural description of smoothing components in the deformation space of cusp singularities, focusing on their connection to Kähler cones of mirror surfaces and associated monodromy groups. Learn about the collaborative research efforts involving Mark Gross, Sean Keel, Ailsa Keating, and graduate students Jennifer Li and Angelica Simonetti, as presented by speaker Paul Hacking from the University of Massachusetts Amherst.