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...
We discuss some regularity results for a class of elliptic equations with coefficients that degenerate or explode on a lower dimensional manifold. The prototype is given by \( -div(|y|^aA(x, y)\nabla ...
The moduli space of stable n-pointed rational curves is a fundamental object in algebraic geometry. Many aspects of the space, such as its intersection theory, have been completely understood. The two...
:We review various notions of self-similar fractal compact sets such as Hutchinson’s, Kigami’s or Kamiyama’s, and see which way most of them can be reached through an inceasing sequence of approximati...
Operads are algebraic structures capturing multi-ary operations. The little disks operads, encoding operations on iterated loop spaces, are fundamental examples. Voronov introduced Swiss-Cheese operad...
In a recent paper, we study the long--time behavior and the stability of the surface diffusion flow of smooth hypersurfaces in the flat torus \(\mathbb T^n\). According to this flow, smooth hypersurfa...
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...
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...
The study of Diophantine equations is one of the oldest problems in mathematics, with many questions that remain open to this day. However, at the start of the 20th century, mathematicians began to re...
