We will discuss some old and new results concerning the
long-time behavior of solutions to the two-dimensional
incompressible Euler equations. Specifically, we discuss
whether steady states can be isolated, wandering for solutions
starting nearby...
One of the central problems of coding theory is to determine the
trade-off between the amount of information a code can carry
(captured by its rate) and its robustness to resist message
corruption (captured by its distance). On the existential
side...
Modern theoretical investigations into the nature of spacetime
are revealing that quantum entanglement plays a crucial role for
resolving several long standing puzzles. Black holes have been
central to these investigations. Quantum models for black...
In this talk, I want to show that in the planar circular
restricted three body problem there are infinitely many symmetric
consecutive collision orbits for all energies below the first
critical energy value. By using the Levi-Civita
regularization...
Liouville field theory was introduced by Polyakov in the
eighties in the context of string theory. Liouville theory appeared
there under the form of a 2D Feynman path integral, which can be
thought of as a measure (or expectation value) over the...
We discuss the existence problem of constant Chern scalar
curvature metrics on a compact complex manifold. We prove a priori
estimates for these metrics conditional on an upper bound on the
entropy, extending a recent result by Chen-Cheng in the...
I shall present two billiard-like systems associated with
a convex hypersurface in a symplectic space, the outer and an
inner ones. The talk will survey the known results and
focus on open problems.
Let K be a knot or link in the 3-sphere, thought of as the ideal
boundary of hyperbolic 4-space, H4. The main theme of my talk is
that it should be possible to count minimal surfaces in H4 which
fill K and obtain a link invariant. In other words...
