We show that any two birational projective Calabi-Yau manifolds
have isomorphic small quantum cohomology algebras after a certain
change of Novikov rings. The key tool used is a version of an
algebra called symplectic cohomology, which is...
At the November workshop, I described a new algorithm to cover
compact, congruence locally symmetric spaces by balls. I’ll discuss
how to compute the nerve of such a covering and Hecke actions on
its cohomology. Joint work with Aurel Page.At the...
For given a Lagrangian in a symplectic manifold, one can
consider deformation of A-infinity algebra structures on its Floer
complex by degree 1 elements satisfying the Maurer-Cartan equation.
The space of such degree 1 elements can be thought of as...
We consider the following question: how many points with bounded
norm can a "non-degenerate" lattice have. Here, by a
"non-degenerate" lattice, we mean an n-dimensional lattice with no
surprisingly dense lower-dimensional sublattices.
Polynomial optimization over hypercubes has important
applications in combinatorial optimization. We develop a
symmetry-reduction method that finds sums of squares certificates
for non-negative symmetric polynomials over k-subset hypercubes
that...
Abstract: Consider the defocusing cubic Schrödinger equation
defined in the 2 dimensional torus. It has as a subsystem the one
dimension cubic NLS (just considering solutions depending on one
variable). The 1D equation is integrable and admits...
Abstract: Arnold diffusion studies the problem of topological
instability in nearly integrable Hamiltonian systems. An important
contribution was made my John Mather, who announced a result in two
and a half degrees of freedom and developed deep...
Abstract: We consider a geometric framework that can be applied to
prove the existence of drifting orbits in the Arnold diffusion
problem. The main geometric objects that we consider are
3-dimensional normally hyperbolic invariant cylinders with...
