In the first part of the talk I will discuss a "holographic" index theorem for compact manifolds with boundary. It relates the index of a boundary value problem to the index of an operator on the boun...
This talk is devoted to the modeling and stability of multi-lane traffic flow in both microscopic and macroscopic frameworks. Firstly, we explore the dynamics of lane changing in microscopic variables...
Abstract: We consider a random walk jumping on a dynamic graph; that is, a graph that changes at the same time as the walker moves. Previous works considered the case where the graph changes via dynam...
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...
In recent times the hydrodynamic behaviour of electrons in graphene has attracted much interest from both the theoretical and experimental viewpoints. The usual approach to graphene hydrodynamics is &...
We prove that a smooth, complex plane curve of odd degree can be defined by a polynomial with real coefficients if and only if it is isomorphic to its complex conjugate; there are counterexamples in e...
Abstract: A spanning tree of a graph G is a connected subset of G without cycles. The Uniform Spanning Tree (UST) is obtained by choosing one of the possible spanning trees of G at random. The Minimum...
Abstract: Earthquakes and tectonic fault slip are among the most hazardous and unpredictable natural phenomena. Fluids play a key role in tectonic faulting and recent research suggests that fluids are...
Quantum simulators were originally proposed to be helpful for simulating one partial differential equation (PDE) in particular – Schrodinger’s equation. If quantum simulators can be useful for simulat...
We derive the heat equation for the thermal energy under diffusive space-time scaling from a purely deterministic microscopic dynamics satisfying Newton equations perturbed by an external chaotic forc...
