Chaidez and Edtmair have recently found the first examples of
dynamically convex domains in R4 that are not symplectomorphic to
convex domains (called symplectically convex domains), answering a
long-standing open question. In this talk we shall...
In 1948, Shannon used a probabilistic argument to show the
existence of codes achieving channel capacity. In 1954, Muller and
Reed introduced a simple deterministic code construction,
conjectured shortly after to achieve channel capacity. Major...
Submanifolds with intrinsic Lipschitz regularity in Carnot
groups (i.e.,
stratified groups endowed with a sub-Riemannian structure) can
be
introduced using the theory of intrinsic Lipschitz graphs started
years
ago by B. Franchi, R. Serapioni and F...
I will talk about the invariants of topologically ordered states
of quantum lattice systems that generalize Berry classes and can be
defined for any gapped state in any dimension. The equivariant
version of such invariants unifies and generalizes...
While convex hypersurfaces are well understood in 3d contact
topology, we are just starting to explore their basic properties in
high dimensions. I will describe how to compute contact homologies
(CH) of their neighborhoods, which can be used to...
Charge-exchange (CX) collisions of the solar wind (SW)
high-ionization-state minor ions with LISM neutrals are responsible
for much of X-ray production in the outer heliosphere. In this
talk, we discuss numerical modeling of the heliospheric CX X...
Multiplier ideals in characteristic zero and test ideals in
positive characteristic are fundamental objects in the study of
commutative algebra and birational geometry in equal
characteristic. We introduced a mixed characteristic version
of the...
Recent years have seen remarkable progress in the field of
Machine Learning (ML).
However recent breakthroughs exhibit phenomena that remain
unexplained and at times contradict conventional wisdom. A
primary reason for this discrepancy is that...
Kinematically, massless particles in Lorentz-invariant theories
are classified by a dimensionful "spin scale"ρ
(2nd Casimir invariant) that characterizes helicity states'
mixing under little group transformations. However, dynamics
for particles...
Motivated by a discovery by Radchenko and Viazovska and by a
work by Ramos and Sousa, we find conditions sufficient for a pair
of discrete subsets of the real axis to be a uniqueness or a
non-uniqueness pair for the Fourier transform. These...
