In this talk, I will present a new bound for solutions to the Poisson problem associated with the weighted one-Laplacian. The Aleksandrov–Bakelman–Pucci (ABP) estimate has long been a fundamental tool...
We investigate geometric and dynamical aspects of hyperbolic lattices arising from regular tilings with 1/p+1/q<1/2. We first characterize finite shapes with minimal perimeter and show that the rat...
The spectral heat content (SHC) measures the total heat contained in a bounded domain at a given time when the initial temperature inside the domain is set to be one, and the temperature outside the d...
A little over a decade ago, Taubes and his disciples started to observe non-compactness phenomena in gauge theories in dimensions three and four that are linked with multi-valued harmonic spinors, 1–f...
La matematica a Roma raggiunge il suo massimo sviluppo nei primi anni '20 del Novecento, quando viene variamente definita La Princeton degli anni '20 (Lefschetz) e Il Paradiso della geometria (Zariski...
Quella delle equazioni dispersive è stata una classe di equazioni differenziali di grande interesse negli ultimi 20-30 anni. Esempi molto rilevanti sono l'equazione di Schrodinger o alcune equazioni d...
Supersymmetric nonlinear sigma models arise in the theory of disordered systems and share key features with O(N)-type models. They also exhibit surprising connections with probabilistic models such as...
In Kähler geometry, the Calabi-Yau theorem establishes the existence and uniqueness of Kähler metrics with prescribed volume form. In this talk, I will present a non-Archimedean version of this theore...
The Weyl energy on four-manifolds is a geometric functional related
to the Chern-Gauss-Bonnet formula. Similarly to Willmore’s functional
for surfaces embedded in the three-dimensional Euclidean spa...
In this talk, I will give a gentle introduction to the theory of motives, as developed by Voevodsky. I will focus on the basic ideas and main properties, explaining how motives are related to algebrai...
La storia della matematica a Roma, dall'Unità di Italia sino al termine della Prima Guerra Mondiale, è strettamente legata alla vita politica, sociale e culturale del Paese. Le sue vicende restituis...
The Dirac equation is one of the fundamental equations in relativistic quantum mechanics, widely used in a large number of applications from physics to quantum chemistry. From the dynamical point of v...
