Events and Activities

A seminal result in learning theory characterizes the PAC learnability of binary classes through the VC dimension. Extending this characterization to the general multiclass setting has been open since the late 1980s.

We resolve this problem by...

To Be Announced

We discuss some recent progress on the model-theoretic problem of classifying the reducts of the complex field (with named parameters and up to interdefinability). The tools we use include Castle’s recent solution of the Restricted Trichotomy...

We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions...

The loop equation for circulation PDF as functional of the loop shape is derived from the Hopf equation. This equation is $\textbf{exactly}$ equivalent to the Schrödinger equation in loop space, with viscosity playing the role of Planck's constant...

We consider a Poisson point process on $R^d$ with intensity lambda for $d>=2$. On each point, we independently center a ball whose radius is distributed according to some power-law distribution mu. When the distribution mu has a finite d-moment...