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...
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...
