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...
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...
In this talk, I will begin with a quick primer to parameterized
complexity, present some key insights from recent hardness of
approximation results in the area, and end with a proof sketch of
the following result: Assuming the Exponential Time...
In large N theories with a gravity dual, generic heavy operators
should be dual to black holes in the bulk. The microscopic details
of such operators should then be irrelevant in the low energy
theory. We look for such universality in the strong...
I’ll describe recent work for approaching certain functional
transcendence problems through a combination of model theory and
differential Galois theory. This is based on joint work with
Blazquez-Sanz, Casale, and Nagloo.
