The long-standing F-Conjecture asserts that there is a very
simple description for the closed cone of effective curves on the
moduli space M_{g,n}\bar of stable n-pointed curves of genus g as
being determined by a finite collection of so-called F...
In 1984, Ryan showed that any smooth Schubert variety in type A
is an iterated fiber-bundle of Grassmannian varieties. Later,
Haiman calculated the generating function for the number of smooth
permutations (equivalently smooth Schubert varieties) of...
I will discuss various applications of a combinatorial model for
the (torus equivariant) quantum K-theory of flag manifolds G/B,
called the quantum alcove model. This is a uniform model for all
Lie types, based on Weyl group combinatorics. It first...
The theory of hierarchically hyperbolic groups, due to
Behrstock, Hagen, and Sisto, was developed by abstracting work of
Masur and Minsky on mapping class groups. Study of the large scale
geometry of the outer automorphism group Out(Fn)
In theoretical computer science, an increasingly important role
is being played by sparse high-dimensional expanders (HDXs), of
which we know two main constructions: "building" HDXs
[Ballantine'00, ...] and "coset complex" HDXs
[Kaufman--Oppenheim...
Given a Lagrangian L, I will discuss the existence of a
neighborhood W of L with the following property: for any
Hamiltonian diffeomorphism f, if f(L) is contained inside W, then
f(L) intersects L. On the one hand, for any symplectic manifold
of...
Central predictions of arithmetic quantum chaos such as the
Quantum Unique Ergodicity conjecture and the sup-norm problem ask
about the mass distribution of automorphic forms, most classically
in terms of their weight or Laplace eigenvalue (for...
I will show that any Schubert or Richardson variety R in a flag
manifold G/P is equivariantly rigid and convex. Equivariantly rigid
means that R is uniquely determined by its equivariant cohomology
class, and convex means that R contains any torus...
We use the min-max construction to find closed hypersurfaces
which are stationary with respect to anisotropic elliptic
integrands in any closed n-dimensional manifold . These surfaces
are regular outside a closed set of zero n-3 dimension. The...
A result of Jan Nekovář says that the Galois action on p-adic
intersection cohomology of Hilbert modular varieties with
coefficients in automorphic local systems is semisimple. We will
explain a new proof of this result for the non-CM part of
the...
