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...