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...
The C0 flux conjecture predicts that a symplectic diffeomorphism
that can be C0
approximated by a Hamiltonian diffeomorphism is itself
Hamiltonian. We describe how the flux conjecture relates to new
instances of the strong Arnol’d conjecture and...
We will discuss a generalization of the celebrated Minimax
Theorem (von Neumann, 1928) for binary zero-sum games. A simple
game which fails to satisfy Minimax is Ephraim Kishon's “Jewish
Poker” (see [1,2] below). In this game, each player picks a...
Interpreting observations of extreme astrophysical phenomena
requires a detailed understanding of particle acceleration in
astrophysical environments. These accelerated particles, known as
cosmic rays, approximately follow a power-law distribution...