I will survey new lower-bound methods in communication complexity
that "lift" lower bounds from decision tree complexity. These
methods have recently enabled progress on core questions in
communication complexity (log-rank conjecture, classical-...
An outstanding problem in smooth ergodic theory is the estimation
from below of Lyapunov exponents for maps which exhibit
hyperbolicity on a large but non- invariant subset of phase space.
It is notoriously difficult to show that Lypaunov exponents...
In this talk we explain how billiard dynamics can be used to relate
a symplectic isoperimetric-type conjecture by Viterbo with an
80-years old open conjecture by Mahler regarding the volume product
of convex bodies. The talk is based on a joint work...
NASA’s GRAIL mission to the Moon was completed in 2012 when both
spacecraft were intentionally “de-orbited” (i.e. crashed) into a
nearside mountainside. This orbital mission measured tiny
variations in the Moon’s gravitational field by continuously...
We will present the project of using the Willmore elastic energy as
a quasi-Morse function to explore the topology of immersions of the
2-sphere into Euclidean spaces and explain how this relates to the
classical theory of complete minimal surfaces...
A translator for mean curvature flow is a hypersurface $M$ with the
property that translation is a mean curvature flow. That is, if the
translation is $t\rightarrow M+t\vec{v}$, then the normal component
of the velocity vector $\vec{v}$ is equal to...
Given a Weinstein domain $M$ and a compactly supported, exact
symplectomorphism $\phi$, one can construct the open symplectic
mapping torus $T_\phi$. Its contact boundary is independent of
$\phi$ and thus $T_\phi$ gives a Weinstein filling of $T_0...
Abstract: I will go over some recent work that I have been
involved in on surface geometry in complete locally homogeneous
3-manifolds X. In joint work with Mira, Perez and Ros, we have been
able to finish a long term project related to the Hopf...