Erdős-style geometry is concerned with combinatorial questions
about simple geometric objects, such as counting incidences between
finite sets of points, lines, etc. These questions can be typically
viewed as asking for the possible number of...
Given n∈ℕ and ξ∈ℝ, let τ(n;ξ)=∑d|ndiξ. Hall and Tenenbaum asked
in their book \textit{Divisors} what is the value of
maxξ∈[1,2]|τ(n;ξ)| for a ``typical'' integer n. I will present work
in progress, carried out in collaboration with Louis-Pierre...
The three problems referred to in the title originate in the
theory of von Neumann algebras, C* algebras, and quantum
information theory respectively. Each of them has been a deep
long-standing open problem in its respective area. Surprisingly,
the...
In the first story we wonder about the ubiquity of the
free field and look at a few characterisation theorems. In the
second story we discuss the mutually benefiting relationship
between the discrete free field and the O(N) spin model. Finally,
in...
In this talk we discuss the existence of a new type of rigidity
of symplectic embeddings coming from obligatory intersections with
symplectic planes. This is based on a joint work with P.
Haim-Kislev and R. Hind.
We consider general two-dimensional autonomous velocity fields
and prove that their mixing and dissipation features are limited to
algebraic rates. As an application, we consider a standard cellular
flow on a periodic box, and explore potential...
Complex dynamics explores the evolution of points under
iteration of functions of complex variables. In this talk I will
introduce into the context of complex dynamics, a new approximation
tool allowing us to construct new examples of entire...
Suppose you have a set S of integers from {1 , 2 , … , N} that
contains at least N / C elements. Then for large enough N , must S
contain three equally spaced numbers (i.e., a 3-term arithmetic
progression)?
Embedded contact homology (ECH) is a diffeomorphism invariant of
three-manifolds due to Hutchings, defined using a contact form.
This very diffeomorphism invariance makes it quite useful when
studying contact dynamics, because it is possible to...
