Previous Special Year Seminar

Many geometric spaces carry natural collections of special submanifolds that encode their internal symmetries. Examples include abelian varieties and their sub-abelian varieties, locally symmetric spaces with their totally geodesic subspaces, period...

Ben Bakker explained to us how to construct moduli spaces of polarized Hodge structures, and then produced period maps associated to families of smooth projective varieties. However, in practice one often encounters a family of smooth 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.

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...

In this talk, I will discuss some effective computations for variations of integral Hodge structures.

Several years ago, with Ren and Javanpeykar-Kühne, I conjectured (in the Shimura setting) that a variation has only finitely many "non-factor"...

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...