The goal of these lectures is to present the fundamentals of
Simpson’s correspondence, generalizing classical Hodge theory,
between complex local systems and semistable Higgs bundles with
vanishing Chern classes on smooth projective varieties.
The goal of these lectures is to present the fundamentals of
Simpson’s correspondence, generalizing classical Hodge theory,
between complex local systems and semistable Higgs bundles with
vanishing Chern classes on smooth projective varieties.
Speaker #1 (Tran): On a projective variety, Simpson showed that
there is a homeomorphism between the moduli space of semisimple
flat bundles and that of polystable Higgs bundles with vanishing
Chern classes. Recently, Bakker, Brunebarbe and...
We give a lower bound on the codimension of a component of the
non-abelian Hodge locus within a leaf of the isomonodromy foliation
on the relative de Rham moduli space of flat vector bundles on an
algebraic curve. The bound follows from a more...
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...
Differential Galois groups are algebraic groups that describe
symmetries of some systems of differential equations. The solutions
considered can live in any differential field and thus a natural
framework to consider such symmetries is the setting...
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.
