Schubert varieties are known to be Frobenius split in positive
characteristic by the work of Mehta and Ramanathan. More recently,
Bhatt showed that the full flag variety for GLn
is a splinter by entirely different methods. In this talk, we
will...
The fundamental group π1(X) is an important invariant of a
complex algebraic variety X. Despite its topological nature,
it is closely connected to the geometry of many algebraic
structures on X. In this talk I want to discuss two
elementary...
Hurwitz moduli spaces of covers of curves of degree d are
classical and well studied objects if one assumes that d! is
invertible and hence no wild ramification phenomena occur. There
were very few attempts to study the wild case. In the most...
A convex toric domain is a 4-dimensional subset of ,
defined as the preimage of a bounded convex region in the
positive quadrant of under the moment map. We consider how
geometric features of such as the curviness of its boundary
and its affine...
In this talk, I will focus on simultaneous non-vanishing results
for Dirichlet L-functions at the central point 1/2. Specifically, I
will describe non-vanishing results (conditional on GRH) for two
L-functions associated to Dirichlet characters in...
Astrophysical black holes are surrounded by accretion disks,
jets, magnetospheres, and coronae consisting of magnetized
relativistic plasma. They produce observable multi wavelength and
multi messenger signals from near the event horizon and it
is...
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 geodesic flow (for the hyperbolic metric) of an infinite
Riemann surface is ergodic if and only if Brownian motion is
recurrent, which is also equivalent to the divergence of the
Poincaré series. Surfaces with ergodic geodesic flows are
most...
Ricci solitons are the self-similar solutions to the Ricci flow,
which is the heat equation for Riemannian metrics, and they model
singularity formation. We survey various estimates for Ricci
solitons in dimension 4. This is mainly the work of...
A classical construction of Mitsumatsu, later generalized by
Hozoori, associates to any (oriented) Anosov flow on a closed
3-manifold M a Liouville structure on the thickening [−1,1]×M. This
construction also extends to suitable taut foliations.
