The no-boundary state in de Sitter offers a compelling framework
for specifying the initial conditions of our universe. Many (but
famously not all) features of the state agree beautifully with
empirical observations and have served as a foundation...
The Poisson summation conjecture of Braverman-Kazhdan, L.
Lafforgue, Ngo, and Sakellaridis is an ambitious proposal to prove
analytic properties of quite general Langlands L-functions using
vast generalizations of the Poisson summation formula. In...
Many geometric spaces carry natural collections of special
submanifolds that encode their internal symmetries. Examples
include abelian varieties and their sub-abelian varieties, locally
symmetric spaces with their totally geodesic subspaces,
period...
I will motivate current work in weak gravitational lensing with
cosmic and astrophysical puzzles. The evolution of dark energy, the
growth of structure and feedback from supermassive black holes are
some of the debated questions. I will describe how...
The Schwarzschild-de Sitter solution can be used to compute the
Hartle-Hawking wavefunction of the universe on a spatial circle
times a sphere. Its norm can be evaluated in the semiclassical
limit and compared to the on-shell action of the Euclidean...
The topology of the universe is unknown, and a typical manifold
will contain nontrivial cycles and boundaries. This is quite
consistent with the observed Lambda CDM cosmology, which does not
imply that we live in a closed universe (including...
The one-loop gravitational path integral around Euclidean de
Sitter space S^D has a complex phase that casts doubt on
a state counting interpretation. Recently, it was proposed to
cancel this phase by including an observer. We explore this
proposal...
Over 50 years ago, Belinski-Khalatnikov-Lifshitz (BKL) argued
that the dynamics of spacetime close to a space like
singularity is chaotic and inhomogeneous. I will revisit the
BKL scenario within a modern understanding of quantum chaos
and...
The framework of quantum reference frames (QRFs) lies at the
crossroads of quantum information, gauge theory, quantum field
theory, and quantum gravity, and has seen rapid progress in recent
years. After introducing the perspective-neutral...
A simple model of topological gravity can be defined by summing
a 3d TQFT over all bulk topologies. I will explain how this sum is
formulated so as to be holographically dual to a well-defined
boundary ensemble. I will then present several explicit...
