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...
The rigorous study of spin systems such as the Ising model is
currently one of the most active research areas in probability
theory. In this talk, I will introduce one particular class of such
models, known as lattice gauge theories (LGTs), and go...
Extremal combinatorics is a central research area in discrete
mathematics. The field can be traced back to the work of Turán and
it was established by Erdős through his fundamental contributions
and his uncounted guiding questions. Since then it has...
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)?
Through the random matrix analogy, Fyodorov, Hiary and Keating
conjectured very precisely the typical values of the Riemann zeta
function in short intervals of the critical line, in particular
their maximum. Their prediction relied on techniques...
In Euclidean geometry, bisectors are perpendicular lines. In
random plane geometry, the situation is more complicated. I will
describe bisectors in the directed landscape, the universal
geometry in the KPZ class. These help answer some open...
