Inflation may have occurred at energies up to 10^16 GeV, far
beyond any terrestrial collider. The "cosmological collider"
program aims to extract the mass spectrum and spin content of
particles present during inflation from non-Gaussian
correlators...
I will talk about a joint work with Antoine Sedillot. We study
sup-norms of sections of metrized line bundles for families of
arithmetic varieties. Using Riemann-Zariski spaces we obtain
formulas that imply new definability results in the context
of...
Numerical simulations of galaxies and the interstellar medium
are now reaching resolutions where small-scale physical processes
can be resolved directly. This raises a natural question: which
pieces of microphysics must be modeled explicitly in...
Constructing completions of period mappings with
significant geometric and Hodge-theoretical meaning is an important
topic in Hodge theory and its applications. There are rich theories
for the classical case in which the period domain is
Hermitian...
The anabelian phenomenon may be viewed as an arithmetic analogue
of Mostow rigidity: it predicts that certain varieties can be
reconstructed from their arithmetic fundamental groups. A
celebrated result of S. Mochizuki shows that hyperbolic
curves...
Given a family X→S, one may consider the
corresponding fiber-wise (quasi-) period integrals as
(multi)-functions on S. Built out of these using a flag variety,
one obtains variation of (mixed) hodge structures giving period
map S→D/Γ. We study the...
I'll start by discussing some work with Binyamini, Schmidt, and
Thomas in which we prove a uniform Manin-Mumford result for
products of CM elliptic curves. I'll show how we apply this to
obtain an effective Andre-Oort result for fibre powers of
the...
We study a non-commutative counterpart Cn(X) of the symmetric
product SymnX of a space X, defined as the space of nxn-matrix
valued points on X. Our main result will be a precise formula for
the cohomology of this space in great generality, but we...
