Mathematics - applications and modelling

Research in this area inolves the mathematical modelling of complex continuous phenomena and the development of appropriate tools for their theoretical as well as numerical treatment. This involves the disciplines of Non-linear Analysis, Calculus of Variations, Optimal Control, Numerical Analysis as well as Mathematical Physics and Differential Geometry. Special emphasis is placed on the modelling of the complex phenomena that one encounters, for example, in the area of Financial Mathematics where the presence of stochastic behaviour requires the tools of Probability and Stochastic Analysis. The area enjoys numerous joint collaborations, both at the national as well as the international level, and its members participate in a variety of research projects involving a number of different sites.

Documents

pdf Brochure di presentazione dell'area  (pdf,  it, 229 KB)
pdf Presentazione Research Day 2017  (pdf,  it, 8484 KB)
Giacomo Albi
Temporary Assistant Professor
Sisto Baldo
Associate Professor
Leonard Peter Bos
Full Professor
Marco Caliari
Associate Professor
Luca Di Persio
Temporary Assistant Professor
Antonio Marigonda
Assistant Professor
Giandomenico Orlandi
Full Professor
Gaetano Zampieri
Research Assistants
Skills
Topic People Description ISI-CRUI
Approximations and expansions - - standard compliant  MSC
Multivariate Polynomial Interpolation Leonard Peter Bos
We study optimal points and their asymptotic distribution for polynomial interpolation on a compact set in R^n Mathematics
Calculus of variations and optimal control; optimization - - standard compliant  MSC
Existence theories Sisto Baldo
Minimal surfaces. Calculus of variations on manifolds. Mathematics
Hamilton-Jacobi theories, including dynamic programming Antonio Marigonda
Nonsmooth Analysis and application to Optmal control. Viscosity solutions of Hamilton-Jacobi equations. Mathematics
Manifolds Sisto Baldo
Antonio Marigonda
Giandomenico Orlandi
Geometric variational and evolution problems: minimal surfaces, motion by mean curvature. Optimal mass transport theory. Mathematics
Optimality conditions. Sisto Baldo
Asymptotics of variational problems. Variational convergences and Gamma Convergence. Singular perturbations of variational problems. Mathematics
Variational principles of physics. Sisto Baldo
Variational problems from condensed matter and particle Physics (e.g. Ginzburg-Landau models for superconductivity, Gross-Pitaevskii model for Bose-Einstein condensation, string theory) and their relation with minimal surfaces. Mathematics
Dynamical systems and ergodic theory - Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems standard compliant  MSC
Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Gaetano Zampieri
Integrable Hamiltonian systems. Lyapunov stability of Hamiltonian equilibria. Nonholonomic versus vakonomic dynamics. Nonlinear nonholonomic constraints. Mathematics
Global analysis, analysis on manifolds - - standard compliant  MSC
Calculus on manifolds; nonlinear operators Gaetano Zampieri
Invertibility of local homeo- and diffeomorphisms. Jacobian problem. Mathematics
Numerical analysis - - standard compliant  MSC
Approximation of matrix exponential Marco Caliari
Polynomial approximation of matrix exponential by interpolation at special nodes. Mathematics
Numerical approximation Leonard Peter Bos
Marco Caliari
We implement algorithms to calculate a numerical approximation of a complicated function, defined either directly by an explicit formula or procedure or else, for example, defined indirectly as the solution of a differential equation of some type. Mathematics
Partial differential equations, initial value and time-dependent initial-boundary value problems Giacomo Albi
Marco Caliari
Solution of non-linear Schrödinger, mean-field and Boltzmann-type equations by pseudo-spectral or meshless methods in space and splitting methods in time. Mathematics
Ordinary differential equations and applications Giacomo Albi
Development of Implicit-Explicit schemes and asymptotic preserving schemes for time dependent problem. Applications in hyperbolic balance laws with diffusive limit and optimal control problems.
Ordinary differential equations - Stability theory standard compliant  MSC
Stability theory Gaetano Zampieri
Lyapunov stability. Mathematics
Partial differential equations - - standard compliant  MSC
Equations of mathematical physics and other areas of application Giacomo Albi
Giandomenico Orlandi
Partial differential equations from condensed matter and particle Physics (e.g. Ginzburg-Landau models for superconductivity and superfluidity, Gross-Pitaevskii model for Bose-Einstein condensation, string theory) and their relation with minimal surfaces and evolution by curvature of interfaces. Boltzmann-type equations and mean-field models for interacting particle systems with applications in socio-economics and biology. Mathematics
Probability theory and stochastic processes - Stochastic analysis standard compliant  MSC
Stochastic analysis Luca Di Persio
Stochastic analysis, theory of stochastic partial differential equations in finite/infinite dimension, randomly interacting particle systems,with applications to Mathematical Finance. Mathematics
Real functions - Inequalities For maximal function inequalities standard compliant  MSC
Inequalities Leonard Peter Bos
We study polynomial inequalities of Markov/Bernstein type for the derivatives of multivariate polynomials. Mathematics
Several complex variables and analytic spaces - Pluripotential theory standard compliant  MSC
Pluripotential theory Leonard Peter Bos
A function defined on C^n is said to be plurisubharmonic if restricted to every complex line it is a subharmonic function of one variable. Pluripodtential Theory is the study of such functions and is, in particular, the correct theory for the study of multivariate polynomials. Mathematics
Projects
Title Managers Sponsors Starting date Duration (months)
Applicazione della teoria del trasporto ottimo alla modellizzazione delle fibre nervose del cervello - Progetto Ricercatori di Recente Afferenza Antonio Marigonda 2/1/10 12
Calcolo delle Variazioni (PRIN 2002 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 12/16/02 24
Calcolo delle Variazioni (PRIN 2004 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 11/30/04 24
Energie di interfaccia e problemi parabolici-iperbolici in ambiente discreto e continuo (GNAMPA 2008 ESTERNO) Giandomenico Orlandi INdAM 2/1/08 12
Fenomeni di evoluzione non lineari suggeriti dalla Fisica e dalla Biologia (GNAMPA 2006 ESTERNO) Giandomenico Orlandi INdAM 1/1/06 12
Fenomeni di propagazione di fronti e problemi di omogeneizzazione (GNAMPA 2010 ESTERNO) Antonio Marigonda INdAM 3/25/10 12
Metodi di controllo ottimo stocastico per l'analisi di problemi di debt-management Antonio Marigonda 3/15/17 12
Metodi di viscosità e metrici per l'omogeneizzazione (GNAMPA 2009 ESTERNO) Antonio Marigonda INdAM 3/1/09 12
Metodi di viscosità, geometrici e di controllo per modelli diffusivi nonlineari (PRIN 2009 ESTERNO) Antonio Marigonda Ministero dell'Istruzione dell'Università e della Ricerca 7/18/11 24
Metodi variazionali nella teoria del trasporto ottimo di massa e nella teoria geometrica della misura (PRIN 2006 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 2/9/07 24
Stochastic Partial Differential Equations and Stochastic Optimal Control with Applications to Mathematical Finance Luca Di Persio 3/21/16 12
Trasporto ottimo di massa, disuguaglianze geometriche e funzionali e applicazioni (PRIN 2008 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 3/22/10 24

Activities

Research facilities