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...
With every bounded prism Bhatt and Scholze associated a
cohomology theory of formal p-adic schemes. The prismatic
cohomology comes equipped with the Nygaard filtration and the
Frobenius endomorphism. The Bhatt-Scholze construction has been
advanced...
Random restrictions are a powerful tool used to study the
complexity of boolean functions. Various classes of boolean
circuits are known to simplify under random restrictions. A prime
example of this, discovered by Subbotovskaya more than 60
years...
Let K be a finite extension of Qp. The Emerton-Gee stack for GL2
is a stack of etale (phi, Gamma)-modules of rank two. Its reduced
part, X, is an algebraic stack of finite type over a finite field,
and can be viewed as a moduli stack of two...
