The $\epsilon$-expansion is a widely used technique to study
aspects of renormalization group flows and critical phenomena. In
this talk, I will discuss recent developments of the
$\epsilon$-expansion in the study of boundary and defect...
In this talk I will introduce a new notion of approximability
for metric spaces that can be seen as a categorification of a
concept introduced by Turing for metric groups and as a
generalization of total-boundedness. I will explain how
recent...
Rational curves are one of the main tools in symplectic geometry
and provide a bridge to algebraic geometry. Complex lines are a
more general class of curve that has the potential to connect
symplectic and complex analytic geometry. These curves are...
Link spectral invariants and their homogenizations have been
defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim
Trifa, we define a linear combination of such quasimorphism and
show that it vanishes on the stabilizer of the equator in...
Cold Neptunes appear to be among the most abundant planets in
the Galaxy, yet their role in shaping planetary systems remains
poorly understood. We study the dynamical evolution of cold Neptune
systems born in resonant chains through disk-driven...
A Hodge structure is a certain linear algebraic datum.
Importantly, the cohomology groups of any smooth projective
algebraic variety come equipped with Hodge structures which encode
the integrals of algebraic differential forms over
topological...
The theory of rigidity for lattices in higher rank semisimple
Lie groups is a powerful and exciting subject, combining methods
from algebra, number theory, geometry and dynamics. One of the most
celebrated results is Margulis' normal subgroup...
Cosmological data has opened up new vistas on fundamental
physics yet it is limited in its scope. While it has given us
tantalizing hints at how the Universe might be expanding, it is
unclear whether it can ever be used to find the
microphysical...
Around 1992, Aldous made the following bold conjecture. Let A be
any set of transpositions in the symmetric group Sym(N). Then
the spectral gap of the Cayley graph Cay(Sym(N),A)
is identical to that of a relatively tiny N-vertex graph
defined by A...
