The finite field Kakeya problem asks about the size of the
smallest set in (F_q)^n containing a line in every direction.
Raised by Wolff in 1999 as a ‘toy’ version of the Euclidean Kakeya
conjecture, this problem is now completely resolved using...
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...
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...
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...
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...
