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...
I will talk about a principal eigenvalue problem for a second-order elliptic operator with a very small diffusion coefficient in one direction. In this regime, how do the principal eigenvalue and the ...
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...
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 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...
Le varietà log-omogenee sono state introdotte da Brion nel 2007, come generalizzazione delle varietà algebriche complesse omogenee complete. Queste ultime sono descritte dal Teorema di Borel-Remmert c...
Uno dei problemi fondamentali della meccanica è descrivere matematicamente i moti, per esempio il moto planetario o delle particelle in un fluido. A parte esempi specialissimi però, non ci si può aspe...
The Flux Problem is a famous problem in condensed matter physics, solved by Lieb. It states that the magnetic flux through each plaquette of a square lattice in 2d (with either OBC/PBC or PBC/PBC) th...
In this talk I present an abstract framework under which Morse theoretical methods can be applied to some non-compact variational problems by computing the difference of topology induced by "critical ...
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...
We study the adiabatic response of open systems governed by Lindblad evolutions (or Gorini-Kossakowski-Sudarshan) and hence affected by some form of friction. In particular, we present the analog of t...
