A Hodge structure is a certain linear algebraic datum.
Importantly, the cohomology groups of any smooth projective
algebraic variety come equipped with Hodge structures which encode
the integrals of algebraic differential forms over
topological...
I will describe recent work in progress on
logarithmic--exponential preparation theorems in analytically
generated sharply o-minimal structures. Our results imply the sharp
o-minimality of $\mathbb{R}_{\exp}$ as well as a uniform version of
Wilkie’s...
I'll focus specifically on point counting results in o-minimal
structures. I'll start with the classical theorem of Pila and
Wilkie and move on to improved versions that only hold in the
"sharp" variant of o-minimality.
Abstract: 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...
Abstract: 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...
Abstract: : Let $g$:$X \rightarrow S$ be a smooth proper family
over algebraic varieties over a number field $K$. Consider the
statement $W(g,p)$: the weight-monodromy conjectures hold for all
fibres of g defined over a finite extension $L/Q_p$. We...
Abstract: 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...
Abstract: 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...
Abstract: The classical Rees construction (of common use in
commutative algebra and Hodge theory) interpolates between
filtrations, viewed as $G_m$-equivariant vector bundles on the
affine line, and their associated gradings. Various
non-abelian...
