In this talk I will present some recent results on the Kirchhoff equation of nonlinear elasticity, describing transversal oscillations of strings and plates, with periodic boundary conditions. We are...
The Kuramoto model is a nonlinear system of ODEs that represents the behavior of coupled oscillators. The coupling is determined by a given graph and pushes the system towards synchronization. An impo...
We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actua...
I shall consider elliptic problems addressing the study of the geometric properties of the solutions. This issue is in general related to the classification of the solutions or to Liouville type theor...
In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We will present two models: the first one...
The classical Courant's nodal domain theorem states that the n-th eigenfunction of the Laplacian on a compact manifold has at most n nodal domains. The same holds for Steklov eigenfunctions on a compa...
We will prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we will obtain a new proo...
Nel seminario presenterò un lavoro in collaborazione con A. Höring e Z. Xie nel quale studiamo la congettura del cono relativa per famiglie di varietà K-triviali con irregolarità nulla. Dopo aver intr...
You've heard the buzz: AI and formalization will revolutionize mathematics. Computers will soon surpass humans in solving olympiad-style problems. Humans will transition from proving research-level t...
We present a new Mountain Pass Theorem for a class of functionals that depends on two arguments which only partially satisfies the Palais-Smale condition. This abstract functional setup will be a...
Onsager proposed a closed-form expression for the free energy of the 2D classical Ising model in 1944. In 1952, Kac and Ward introduced an alternative elegant method of combinatorial nature. Kager, Li...
Advection dominated problems represent still nowadays a great challenge for the Model Order Reduction community, because of their intrinsic difficult nature. In this talk we will focus on hyperbolic p...
