CMSA Geometry and Mathematical Physics Seminar: Towards a Hodge theoretic mirror symmetry for punctured surfaces

In their 1992 paper, “Ising Model and N=2 Supersymmetric Theories,” Cecotti and Vafa asserted that a certain hyperelliptic configuration space of chiral fields is mirror to the Ising model. Today, this statement can be understood as an isomorphism of variations of noncommutative Hodge structures. In this talk, I will argue how the work of Cecotti and Vafa could be connected to homological mirror symmetry for punctured surfaces, thereby providing a Hodge theoretic perspective on the subject.