Analysis and Mathematical Physics

The Yang-Mills-Higgs (YMH) model plays a central role in several areas of mathematics, including analysis, geometry, and probability theory. In this talk, we implement the stochastic quantization procedure for the YMH model in two dimensions. That...

We give several constraints on the dissipation measure arising in the inviscid limit of two-dimensional incompressible fluids under minimal assumptions on the initial datum. None of them is replicable in three dimensions, highlighting the non...

TBA

Optimal bubble cluster problems concern the study of partitions of $\mathbb{R}^n$ into a fnite collection of chambers, some with finite volume and some with infinite volume. One looks for local minimizers of interfacial area subject to volume...

For the passive vector equation, the fast dynamo conjecture predicts exponential-in-time growth of the $L^2$ norm of the solution under the Lipschitz flow generated by a vector field, at a rate independent of the resistivity. We prove this...