Previous Special Year Seminar

We will first quickly recall basic facts on the tree of SL_2 over a field K with a discrete valuation v, following Serre's book. We will then generalize the geometric interpretation given in that book for curves to a higher dimensional situation...

For low degree K3 surfaces there are several way of constructing and compactifying the moduli space (via period maps, via GIT, or via KSBA). In the case of degree 2 K3 surface, the relationship between various compactifications is well understood by...

We will first quickly recall basic facts on the tree of SL_2 over a field K with a discrete valuation v, following Serre's book. We will then generalize the geometric interpretation given in that book for curves to a higher dimensional situation...

Inspired by the elementary notion of graph chordality, we introduce the notion of toric chordality, which naturally gives a tool to to study the geometry and combinatorics of cohomology classes of toric varieties and the weight algebras of polytopes...

A Cartwright-Steger surface is a complex ball quotient by a certain arithmetic cocompact group associated to the cyclotomic field $Q(e^{2\pi i/12})$, its numerical invariants are with $c_1^2 = 3c_2 = 9, p_g = q = 1$. It is a cyclic degree 3 cover of...

In this talk I will present some joint work with Jeff Achter concerning the problem of determining when the cohomology of a smooth projective variety over the rational numbers can be modeled by an abelian variety. The primary motivation is a problem...

A famous result of Borel says that the cohomology of $\mathcal A_g$ stabilizes. This was generalized to the Satake compactification by Charney and Lee. In this talk we will discuss whether the result can also be extended to toroidal...

In this talk, I will begin by recalling the classification of normal functions over $\mathcal M_{g,n}$, the moduli space of $n$-pointed smooth projective curves of genus $g$. I'll then explain how they can be used to resolve a question of Eliashberg...

A decade ago, John Morgan and I classified all integral weight 3 VHS of Hodge type (1,1,1,1) which can underly a family of Calabi-Yau three folds over the thrice-punctured sphere, subject to conditions on monodromy coming from mirror symmetry. There...