Video Lectures

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...

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...

I will explore one of the most profound open question in particle physics, focusing on some exciting directions of my ongoing research activity: the strong CP problem. I will begin with an overview of the strong CP problem, highlighting proposed...

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 evolution of planets and planetary systems depends on the environments created by their host stars in a number of ways.  In this talk, I will discuss several observable impacts of stellar winds, radiation pressure, and non-thermal ionizing...

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...