Since the work of Jacobi and Siegel, it is well known that Theta
series of quadratic lattices produce modular forms. In a vast
generalization, Kudla and Millson have proved that the generating
series of special cycles in orthogonal and unitary...
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...
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...
