The East model is a one-dimensional interacting particle system with non attractive spin-flip dynamics. In the physics literature, it is a key example of a model with glassy features. Here we take thi...
Abstract: Engineering, intended as the capability of producing innovation and new technology, pays an important tribute to mathematics. It is well known how the increasing computer power open th...
Abstract: Graphene is a two-dimensional material with a unique set of properties, many of which rely on its planar two-dimensional structure. In many applications, graphene is supported on a substrate...
Abstract: Today’s 3D printers are likely to revolutionize personal fabrication, with their hardware improving everyday and their cost getting lower. In this walk, I will present my work in using 3D pr...
The asymptotic decay rate and other qualitative features of solutions to parabolic equations set in noncompact domains of RN, or Riemannian manifolds, depend in general on a suitable notion of the geo...
We discuss some recent results related to the homogeneous Dirichlet problem for the infinity Laplace equation with constant source in a bounded domain. We characterize the geometry of domains for whic...
We consider vectorial variational problems of the form E[u]=∫W(Du)dx, typical for example of nonlinear elasticity and plasticity, which include constraints on the determinant. Specifically, the ener...
Segregation phenomena occurs in many areas of mathematics and science: from equipartition problems in geometry, to social and biological processes (cells, bacteria, ants, mammals) to finance (sellers ...
The well-studied power-law-nonlinearity elliptic PDE is known to exhibit a variety of interesting effects, including non-existence, non-uniqueness and concentration phenomena. The application of forma...
In the 80s, De Giorgi introduced the notion of abstract gradient flows, which allowed to define a notion of solutions to ordinary differential equations of the form x' = −grad F(x) on metric spaces ...
We discuss an epsilon-regularity result at the endpoint of connected arcs for 2-dimensional Mumford-Shah minimizers obtained in a joint work with C. De Lellis (U. Zuerich). As an outcome of our analys...
