Homological stability is now well established as an organizing
principle and computational tool in algebraic topology and other
areas. In many cases it is of interest to obtain homological
stability with twisted coefficients, and the standard choice...
This talk is a discussion about the extremal points of the unit
ball with respect to the Hessian-Schatten variation seminorm, i.e.
the total variation of the second distributional differential with
respect to the Schatten matrix norm. The main...
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...
