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Mathematical Analysis, Probability and Statistics

Mathematical Analysis

Mathematical analysis is one of central branches of mathematics and it is a unifying language of modern sciences. Mathematical analysis develops both from its own open problems and needs for a theoretical unification, and under the stimulus from other branches of mathematics, of natural sciences and of the most diverse applications.

The analysts of our department work in a variety of research areas, Partial Differential Equations and function spaces in which PDE's and their solutions live.

Among the topics studied by the analysis group are: PDE's with an underlying subRiemannian structure and the study of subRiemannian geometry; geometric analysis of PDE's; spectral and microlocal analysis; differential equations in Banach spaces; function spaces and related operators.

Probability and Statistics

Probability and Statistics have great theoretical interest and also applications in almost all sciences and aspects of reality.
Probability quantifies the uncertainty, while Statistics which, at least in the Bayesian setting, can be considered as an area of Probability, allows to get probabilistic evaluations from real data.

The probabilists of our department work in a variety of research areas, especially related to the theory of stochastic processes, random fields and disordered systems.

The topics studied by the probability group are: Gibbs random fields; percolation theory and random walks in a random environment, in particular on directed random graphs; stochastic differential equations for diffusion and jump processes; linear and non-linear Kolmogorov-Fokker-Plank equations; optimal stopping problems; numerical methods and analytical approximations of transition densities; applications to mathematical finance.

Abenda Simonetta

Finite and infinite dimensional integrable Hamiltonian systems and nonlinear waves.

Albano Paolo

Arcozzi Nicola

Holomorphic function spaces. Analysis in metric spaces. Potential theory.

Baldi Annalisa

Forme differenziali in Gruppi di Carnot e applicazioni. Equazioni alle derivate parziali subellittiche. Omogenizzazione.

Bonfiglioli Andrea

Potential Theory. Degenerate-elliptic operators on Lie groups. Carnot groups and subelliptic Laplacians.

Bove Antonio

Campanino Massimo

Campi aleatori di Gibbs. Teoria della percolazione. Passeggiate aleatorie su grafi aleaori.

Cicognani Massimo

Citti Giovanna

Cupini Giovanni

Calculus of Variations. Partial differential equations.

Dore Giovanni

Favini Angelo

Equazioni di evoluzione degeneri. Problemi inversi. Equazioni differenziali operatoriali.

Ferrari Fausto

Franchi Bruno

Grammatico Cataldo

Guidetti Davide

Lanconelli Ermanno

Liess Otto Edwin

Manfredini Maria

Nonlinear sub-elliptic equations. Fundamental solutions. Surfaces in nonhomogeneous Lie groups.

Martino Vittorio

Montanari Annamaria

Pseudoconvessità ed equazioni di assegnata curvatura di Levi. Equazioni alle derivate parziali subellittiche lineari e non lineari.

Morbidelli Daniele

Analisi geometrica in spazi subriemanniani.

Mughetti Marco

Ipoellitticità. Equazioni alle derivate parziali. Analisi microlocale

Negrini Paolo

Obrecht Enrico

Parmeggiani Alberto

Geometric analysis of PDEs. Spectral theory. Solvability and a priori estimates for systems of PDEs.

Pascucci Andrea

Stochastic differential equations and hypoelliptic equations. Diffusions and stochastic processes with jumps. Applications to mathematical finance.

Ravaglia Carlo

Scornazzani Vittorio

Sordoni Vania

Tesi Maria Carla

Mathematical models of the Alzheimer's disease. Differential forms in Carnot groups and applications. Homogenization.

Uguzzoni Francesco

Second order partial differential equations with nonnegative characteristic form.

Venni Alberto

Methods of Operator Theory. Linear Partial Differential Operators.