A classical idea going back at least to work of Leon Simon (1997) is that Liouville theorems for solutions to elliptic or parabolic PDEs are equivalent to Schauder-type regularity estimates. In this t...
Exponential sums over finite fields are essential ingredients in the solution of many arithmetic problems. Their study often relies on algebraic geometry, and especially on Deligne's Riemann Hypothesi...
The Stochastic Sandpile Model is an interacting particle system introduced in the physics literature to study the mechanism of self-organized criticality. This model undergoes a phase transition when ...
The theory of currents provides a powerful framework for studying geometric and variational problems where classical oriented surfaces are insufficient. Metric currents generalize this theory to space...
The theory of currents provides a powerful framework for studying geometric and variational problems where classical oriented surfaces are insufficient. Metric currents generalize this theory to space...
On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning ...
On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning ...
A strong geometry with torsion is a Riemannian manifold carrying a metric connection
with closed skew-symmetric torsion. In the seminar I will first review general properties of metric connections...
In analytic number theory one needs to bound sums of oscillating functions, such as the Mobius function. Over function fields these are trace functions of sheaves, so their sums are controlled, in vie...
I will review some recent developments about the 2D classical Ising model focusing on the method of Kac and Ward. In joint work with Daniel Ueltschi, we have extended this method to systems with negat...
Nonlocal minimal surfaces are the fractional counterpart of the classical minimizers of the perimeter functional. A special subclass is given by nonlocal minimal graphs, namely nonlocal minimal surfac...
