Mathematics

In this talk, I will introduce the space of random measures $\mathcal{P}_p(\mathcal{P}_p(X))$, endowed with the Wasserstein-on-Wasserstein metric, where $(X, d)$ is a complete separable metric space. In this setting, we prove a metric superposition principle, that will allow us to recover important geometric features of the space. When $X$ is $\mathbb{R}^d$, we will se also...

One of the central problems in mathematical physics is the rigorous construction of the quantum Yang-Mills theory on \mathbb{R}^4 and the proof of the existence of a positive mass gap. In this talk, I will present some recent progress on the lower dimensional cases T^2 and T^3. In particular, we construct gauge orbit spaces \mathcal{A}/~ where...