I will discuss questions pertaining to geometric unlikely
intersections and transcendence in the setting of torii in positive
characteristic. This is based on work in progress joint with Anup
Dixit, Philip Engel, and Ruofan Jiang.
I'll talk about the o-minimal structures R_LN and R_{LN,exp}
where one has an effective form of the finiteness property of
o-minimality. Unlike the more classical structure of Pfaffian
function, R_{LN,exp} contains the period integrals for
aribtrary...
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...
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.
A compact hyperkahler manifold is a higher-dimensional analog of
a K3 surface; Lagrangian fibrations of hyperkahler manifolds are
higher-dimensional versions of elliptic fibrations of K3 surfaces.
A result of Voisin shows that these fibrations yield...
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 Tsimerman proved a version...
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...
