In the 60's Almgren initiated a program for developing Morse theory
on the space of flat cycles. I will discuss some simplifications,
generalizations and quantitative versions of Almgren's results
about the topology of the space of flat cycles and...
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...
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...
Abstract: We will explain how to prove properness of a complete
embedded minimal surface in Euclidean three-space, provided that
the surface has finite genus and countably many limit ends (and
possibly compact boundary).
Abstract: We define a relative entropy for two expanding
solutions to mean curvature flow of hypersurfaces, asymptotic to
the same smooth cone at infinity. Adapting work of White and using
recent results of Bernstein and Bernstein-Wang, we show that...
