Events and Activities

What is the "right" topological invariant of a large point cloud $X$? Prior research has focused on estimating the full persistence diagram of $X$, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient...

I will describe recent progress in determination of asymptotic behavior in random constraint satisfaction problems, including the independent set problem on random graphs, random regular NAE-SAT, and random SAT. The results include sharp phase...

In the mid 80's, Bourgain asked the following question: Is there a universal constant $c>0$ such that every compact convex set $K$ in $R^n$, of unit volume, must contain a slice (namely, a set of the form $K \cap H$ for some affine hyperplane $H$)...

In the mid 80's, Bourgain asked the following question: Is there a universal constant $c>0$ such that every compact convex set $K$ in $R^n$, of unit volume, must contain a slice (namely, a set of the form $K \cap H$ for some affine hyperplane $H$)...

(This lecture is related to the preceding lecture, but I will try to make it self-contained as much as possible.) In this lecture I will elaborate on some of the existing mathematical approaches to the study of random CSPs, particularly involving...