Workshop on Special Cycles and Related Topics

I'll talk about some classical problems around orthogonal polynomials and harmonic analysis that fall into the "unlikely intersection" paradigm: they can be reformulated as questions about counting integers in definable sets whose algebraic parts...

Given a local system on a complex algebraic variety, what are the subvarieties on which the monodromy drops? The talk will discuss these monodromy special loci, a natural generalisation of (the positive period dimension components of) the Hodge loci...

To show that the Gamma function, restricted to the positive real half-axis, generates an o-minimal structure over the real field, we had to show (in collaboration with Lou van den Dries) that the expansion of the real field by all functions that are...

The Zilber-Pink conjecture is a far reaching and widely open conjecture in the area of "unlikely intersections" generalizing many previous results in the area, such as the recently established André-Oort conjecture. Recently the ``G-functions method...

The classical Rees construction (of common use in commutative algebra and Hodge theory) interpolates between filtrations, viewed as Gm

-equivariant vector bundles on the affine line, and their associated gradings. Various non-abelian versions have...

From the outset, topology has played an important role in the study of o-minimal structures. The central focus has been on developing the theory of o-minimality as a framework for 'tame topology', built upon the natural and well-behaved underlying...

Let C be a curve defined over a finite field, and let X/C

be a non-isotrivial family of K3 surfaces. In joint work with Maulik-Tang, under a compactness assumption (an assumption removed in later work by Tayou), we prove that if the K3 surface is...

A classical theorem due to Borel states that every holomorphic map from a poly-punctured disk into a Shimura variety (with torsion-free level structure) extends holomorphically across the punctures to the minimal compactification. As a consequence...

I will talk about mod p versions of the Mumford—Tate and André—Oort conjectures. Via a notion of formal linearity, the two conjectures, together with a third one (modpAx—Lindemann), are closely entangled with each other — much closer than their char...

I will discuss work in progress with M. Orr (Manchester) and G. Papas (Weizmann) on the Zilber-Pink conjecture for $Y(1)^3$. This is known for so-called asymmetric curves by the 2012 work of Habegger-Pila. More recently, an approach known as the G...