In this talk we discuss the cubic wave equation in three
dimensions. In three dimensions the critical Sobolev exponent is
1/2. There is no known conserved quantity that controls this norm.
We prove unconditional global well-posedness for radial...
Geodesic nets on Riemannian manifolds is a natural
generalization of geodesics. Yet almost nothing is known about
their classification or general properties even when the ambient
Riemannian manifold is the Euclidean plane or the round
2-sphere.
I will describe a new family of symplectic capacities defined using
rational symplectic field theory. These capacities are defined in
every dimension and give state of the art obstructions for various
"stabilized" symplectic embedding problems such...
Positive geometries are real semialgebraic sets inside complex
varieties characterized by the existence of a meromorphic top-form
called the canonical form. The defining property of positive
geometries and their canonical forms is that the residue...
A matroid is an abstract combinatorial object which generalizes
the notions of spanning trees, and linearly independent sets of
vectors. I will talk about an efficient algorithm based on the
Markov Chain Monte Carlo technique to approximately...
Deep learning has led to rapid progress in open problems of
artificial intelligence—recognizing images, playing Go, driving
cars, automating translation between languages—and has triggered a
new gold rush in the tech sector. But some scientists...
Deep learning has led to rapid progress in open problems of
artificial intelligence—recognizing images, playing Go, driving
cars, automating translation between languages—and has triggered a
new gold rush in the tech sector. But some scientists...
Deep learning has led to rapid progress in open problems of
artificial intelligence—recognizing images, playing Go, driving
cars, automating translation between languages—and has triggered a
new gold rush in the tech sector. But some scientists...
