I will give a gentle introduction with several examples to the following topic: Yau-Tian-Donaldson conjecture states that a polarised manifold $(X,L)$ admits a cscK metric in $c_1(L)$ if and only if $...
This talk is devoted to semilinear parabolic equations on infinite weighted combinatorial graphs. We will address finite-time blow-up phenomena, considering both arbitrary initial data and sufficientl...
We consider the Erdős-Rényi graph G in its critical regime when its expected degree d scales like the logarithm of its number of vertices. On this critical scale, G undergoes a connectivity transitio...
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...
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...
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...
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...
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...
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...
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...
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 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...
