The talk will be on recent progress in a series of joint papers
with Filip Živanović, about a large class of non-compact symplectic
manifolds, which includes semiprojective toric manifolds, quiver
varieties, and conical symplectic resolutions of...
Mathematician Hel Braun, Member (1947–1948) in the School of
Mathematics, left a remarkable legacy, despite facing formidable
challenges. While Braun's mathematical contributions remain
important, her story has been mostly forgotten. In this talk...
I will give an overview of recent progress in random
multiplicative functions (random models for multiplicative
functions) and their connection to the study of the
Fyodorov-Hiary-Keating conjecture and Polya's question on
nonnegative character sums...
Gas-rich environments are ubiquitous in various scales, from
protoplanetary disks to star clusters and galaxies. Dynamics in
gas-rich environments are substantially different and give rise to
unique astrophysical phenomena, along with enhancing the...
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...
