Video Lectures

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...

An exact Lagrangian in a cotangent bundle that coincides with

a cotangent fiber outside a compact set, and is disjoint from at least

one cotangent fiber is called a nearby Lagrangian fiber. I will explain

joint work in preparation with Yash Deshmukh...

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...

We will survey various recent results around the distribution of the Hodge locus of a (mixed) variation of Hodge structures. Various concrete applications to moduli spaces will also be presented.

We prove that an algebraic flat connection has ℝan, exp

-definable flat sections if and only if it is regular singular with unitary monodromy eigenvalues at infinity, refining previous work of Bakker–Mullane. This provides e.g. an o-minimal...