Main topics

a) Analytical study of partial differential equations.Geometrical tools for elliptic and parabolic boundary problems,p-Laplacian. Properties of operators in non standard functional spaces and their application to differential equations. Asymptotic analysis of non linear hyperbolic operators in various domains, including networks. Reconstruction of unknown terms in heat flows on the interface solid-liquid.

b) Asymptotic analysis of Poisson systems with application to wireless and social networks. Point processes, large deviations, Malliavin calculus, functional inequalities, percolation, evolutionary modelsbased on the game theory.

c) Traffic and evolution problems on networks. Setting and development of mathematical models and numerical algorithms to forecast car traffic evolution on road networks. Mathematical modelsto forecast and control of pedestrian flows. Analysis of water flow in a network of channels.

d) Differential models for biological systems. Models of organization and transport in the cell, stem cells and tumor cells, diffusion phenomena, chemotaxis; drug release and biomedical devices.Regeneration of biological tissues and growth of embryonic structures. Transmission of intracellular signals. Models for the therapeutic use of DNA tumor vaccines. Mutation models.

e) Control and differential games. Fast numerical methods for Hamilton-Jacobi equation for optimal control and differential games.

f) Forecasting of the damage on monuments. Chemical damage of stone and metal materials. Biological damage

g) Analytical and numerical study of differential, integral, andintegro-differential equations. Analytical study, numerical aspects (convergence and stability), computing. Applications to: population dynamics, fracture mechanics, dust dynamics in fusion plants. Well-balanced schemes for hyperbolic and parabolic equations, with extensions to kinetic equations and radiative transfer.

h) Mathematical methods and models for economy, actuarial sciences and mathematical finance. Development of models for duopoly/oligopoly. Stochastic models and algorithms for risk management in the actuarial sciences. Numerical computing of solutions of partial differential and integro-differential equationsfor pricing financial derivatives with stochastic volatility.

List of funded projects:

ContrattoZero+, PON MIE, PON Intour, Progetto Premiale Mathtech, GNCS 2015“Conservazione numerica di proprietà qualitative delle soluzioni di problemi differenziali”, progetto Giovani 2015 del GNFMdell'IndAM "Dinamica di sistemi complessi infinito dimensionali con applicazioni in Fluidodinamica, Economia e Biologia".

1. Fabrizio Clarelli, Cristiana Di Russo, Roberto Natalini, Magali Ribot, A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity, to appear in Mathematical Medicine and Biology 2016; first published online July 17, 2015, doi:10.1093/imammb/dqv024