May 24 -- Lucas Castello Branco

Motivated by mirror symmetry for the moduli space of Higgs bundles, we discuss the construction of Lagrangian subvarieties that arise from symplectic representations. In particular, for the standard representation of the symplectic group, we show that this corresponds to a particular irreducible component of the nilpotent cone of the Hitchin system using an auxiliary (spinor) moduli space and Morse theory techniques.

May 24 -- John Alexander Cruz Morales

In this talk I will discuss some speculative ideas (work in progress) about the study of mirror maps for Calabi-Yau hypersurfaces from the perspective of model theory (a branch of mathematical logic). I will propose that some of the arithmetic and geometric properties of those mirror maps can be understood from purely model theoretic concepts like categoricity. The case of elliptic curves will be discussed in detail since it is the motivation of my proposal. No knowledge of model theory will be assumed so I will introduce the notions needed for the talk.