In the search for simple, solvable models of quantum cosmology
it is useful to focus on general relativity in 2+1 dimensions,
where - due to the absence of local degrees of freedom - there is
some hope that we can say something precise. I will...
In 2023, Raghu Meka and I proved a substantially improved bound
on the size of the smallest set of integers in [N] which contains
no 3-term arithmetic progression. Since then, it has become clear
that the main new ideas from that work are in fact...
In this talk I will first define the space of h-cobordisms
associated to a manifold M. This space is known to have many
non-trivial homotopy groups and in stable range (they can often be
computed using Waldhausen's algebraic K-theory of spaces). I...
We will discuss an inductive approach to determining the
asymptotic number of G-extensions of a number field with bounded
discriminant, and outline the proof of Malle's conjecture in
numerous new cases. This talk will include discussions of
several...
Pulsar timing array (PTA) experiments aim to detect
nHz-frequency gravitational waves using high-precision timing of
millisecond pulsars. Multiple PTA collaborations have recently
reported evidence for a stochastic gravitational wave
background...
A valuation is a finitely additive measure on the class of all
convex compact subsets of Rn. Over the past two decades, a number
of structures has been discovered on the space of translation
invariant smooth valuations. Recently, these findings...
Influential work of Hodge from the 1940s led the way in using
Gröbner bases to combinatorially study the Grassmannian. We follow
Hodge's approach to investigate certain subvarieties of the
Grassmannian, called positroid varieties. Positroid...
We prove ''reasonable'' quantitative bounds for sets in ℤ2
avoiding the polynomial corner configuration
(x,y),(x+P(z),y),(x,y+P(z)), where P is any fixed
integer-coefficient polynomial with an integer root of multiplicity
1. This simultaneously...
In this overview talk we will explore a variational approach to
the problem of Spectral Minimal Partitions (SMPs). The
problem is to partition a domain or a manifold into k subdomains so
that the first Dirichlet eigenvalue on each subdomain is as...
