We present a survey of nonlinear elliptic equations with nonlocal interactions. These equations describe the collective behavior of self-interacting many-body systems at different scales, from atoms a...
I will first present a convergence result for solutions of Allen-Cahn type systems with a multiple-well potential involving the usual fractional Laplacian in the regime of the so-called nonlocal mini...
The aim of this seminar is to highlight the combinatorial aspects that arise from studying the compactifications of the moduli space of smooth curves. We will provide an overview of the construction o...
We investigate the massive Sine-Gordon model in the finite ultraviolet regime on the two-dimensional Minkowski spacetime with an additive Gaussian white noise. In particular we construct the expectati...
I will report on a joint work with Amine Marrakchi. Since the early days of Tomita-Takesaki theory, it is known that a von Neumann algebra that admits a state with trivial centralizer must be a type I...
Like many discrete statistical mechanics models, stochastic PDEs can exhibit a “critical dimension” beyond which their large-scale behaviour is expected to be trivial (i.e. governed by Gaussian fluctu...
In questo seminario presenterò alcuni problemi di ottimizzazione di forma per equazioni ellittiche con condizioni al bordo di tipo Robin. Problemi di questo tipo, nel caso di condizioni di tipo Dirich...
The idea of moduli space is quite intuitive, you have surely encountered it multiple times. We will present a general overview of moduli spaces in an algebraic context, stressing the categorical point...
I will talk about a new cohomology theory for algebraic varieties in positive characteristic, called edged crystalline cohomology. This is a generalisation of crystalline cohomology and depends on the...
