Spectral invariants defined via Embedded Contact Homology (ECH)
or the closely related Periodic Floer Homology (PFH) satisfy a Weyl
law: Asymptotically, they recover symplectic volume. This Weyl law
has led to striking applications in dynamics...
The braid group B_{2g+1} has a description in terms of the
hyperelliptic mapping class group of a curve X of genus g.
This equips it with an action on V = H_1(X), and we may produce a
wealth of new representations S^{\lambda}(V) by applying
Schur...
A basic question in arithmetic statistics is: what does
the Selmer group of a random abelian variety look like? This
question is governed by the Poonen-Rains heuristics, later
generalized by Bhargava-Kane-Lenstra-Poonen-Rains, which predict,
for...
I will discuss the following conjecture: an irreducible Q¯
ℓ-local system L on a smooth complex algebraic variety S arises in
cohomology of a family of varieties over S if and only if L can be
extended to an etale local system over some descent of S...
I will weave three separate threads. The first will be to
describe recent and ongoing results from the Dark Energy
Spectroscopic Survey. I will present the BAO results from the early
DESI data, and some of the preparatory work for the Year 1 data.
I...
High dimensional expanders are an exciting generalization of
expander graphs to hypergraphs and other set systems.
Loosely speaking, high dimensional expanders are sparse
approximation to the complete hypergraph. In this talk, we’ll
give a gentle...
An old problem in classical mechanics is the existence of
periodic flows within specific classes of Hamiltonian systems such
as geodesic and magnetic flows, and central forces. In the last
years, interest in this problem has been revitalized since...
In this work we prove a high dimensional analogue of the beloved
Goldreich-Levin theorem (STOC 1989), which is the first local
list-decoding algorithm. We consider the following
algorithmic problem: given oracle access to a function f:Zmq⟶Znq
such...
