Abstract: In this talk, we explore large-scale interacting systems that explain macroscopic phenomena through the movement of microscopic particles. These systems are modeled by discrete lattices wher...
On non-smooth domains, elliptic regularity for solutions of boundary value problems, measured by Sobolev norms, will only hold for a restricted set of regularity indices, due to singularities of the s...
The regularity of solutions of the Dirichlet problem for the Laplace operator in corner domains is limited by the existence of harmonic functions that are zero on the boundary of some tangent cones. T...
Abstract: La nozione di entropia topologica, derivante dalla teoria dell’informazione, è uno strumento fondamentale per comprendere la complessità di un sistema dinamico.Quando il sistema ...
We consider a Lane-Emden problem in a smooth bounded domain. When the exponent p of the nonlinearity is large, the existence and multiplicity of solutions strongly depend on the geometric properties o...
Abstract: Many systems of interest in the applied sciences share the common feature of possessing multiple scales, either in time or in space, or both. Some approaches to modelling focus on one scale ...
We study \(A_g\), the moduli space of principally polarized abelian varieties of dimension \(g\). The tautological ring, generated by the Chern classes of the Hodge bundle, was fully determined by Ger...
The study of singularities of minimal surfaces is a fundamental problem in Geometric Analysis, which, for decades, has been fueling some beautiful research in Differential Geometry, Geometric Measure ...
We consider solutions to \(-\Delta_p u=f(x)\) in \(\Omega\), when \(p\) approaches the semilinear limiting case \(p = 2\) and we get third order estimates. As a consequence we deduce improved regulari...
The development of efficient reduced order models (ROMs) from a deep learning perspective enables users to overcome the limitations of traditional approaches. One drawback of the techniques based on c...
According to the uniformisation theorem, in complex dimension one, there is an intimate connection between complex and hyperbolic structures. However, in higher dimensions, the two geometries diverge....
When minimizing a regularized functional - i.e., one of the form \(H(u) = F(u) + \alpha G(u)\), where \(G\) is a regularization term and \(\alpha\) is the regularization parameter - one generally expe...
