Special Year 2014-15: The Topology of Algebraic Varieties

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...

This will be an expository talk, mostly drawn from the literature and with emphasis on the several parameter case of degenerating families of algebraic varieties.

In the theory of algebraic cycles, the archimedean height is a real number attached to null-homologous non-intersecting algebraic cycles on a smooth projective variety \(X\) whose dimensions add up to one less than the dimension of \(X\). For...

The Andre-Oort conjecture describes the expected distribution of special points on Shimura varieties (typically: the distribution in the moduli space of principally polarized Abelian varieties of points corresponding to Abelian varieties with...

The main tool in Ngô's proof of the Langlands-Shelstad fundamental lemma, is a theorem on the support of the relative cohomology of the elliptic part of the Hitchin fibration. For $\mathrm{GL}(n)$ and a divisor of degree $ > 2g-2$, the theorem says...

The Andre-Oort conjecture describes the expected distribution of special points on Shimura varieties (typically: the distribution in the moduli space of principally polarized Abelian varieties of points corresponding to Abelian varieties with...