italianoITA
Head of Dept:  Prof. Giulio Magli
Vice-Head of Dept:  Prof. Gabriele Grillo
Department Manager:  Dr.ssa Franca Di Censo
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Research Groups

ANALYSIS OF VARIATIONAL AND DIFFERENTIAL PROBLEMS - OPERATORS THEORY
ACTIVITY DESCRIPTION

Main research topics of the group refer to: variational methods for image segmentation and inpainting; shape optimization: geometric-functional inequalities, optimal partitions; free discontinuity problems; noncoercive minimum problems in continuum mechanics; free boundary problems associated to variational inequalities; convex analysis and control problems. Spectral analysis of scalar operators and functional calculus based on holomorphic functions theory are cornerstones of Functional Analysis with many applications to the theory of differential equations. Since 2006 a new spectral theory was introduced (based on the notion of S-spectrum) for vector-valued operators, providing a hyper-holomorphic vector functional calculus that allows to introduce a new class of fractional diffusion problems.

SKILL
  • Calculus of Variations.
  • Variational methods for image segmentation and inpainting.
  • Dimension reduction in nonlinear elasticity and recession functional.
  • Shape optimization problems and geometric-functional inequalities.
  • Free discontinuity problems.
  • Optimal partitions.
  • Hyper-holomorphic functional calculus and spectral decomposition of vector linear operators.
  • Fractional powers of vector-valued operators and new classes of problems related to fractional diffusion.
COMPONENTS OF THE GROUP
1 TOMARELLI Franco PO
2 CAROCCIA Marco RTDA
3 CAVAGNARI Giulia RTDA
4 COLOMBO Fabrizio PO
5 FRAGALÀ Ilaria PO
6 LAENG Enrico PA
7 MALUTA Elisabetta PA
8 MARCHIONNA Clelia PA
9 PIOVANO Paolo RTDB
10 SOMAGLIA Jacopo RTDA
ANALYSIS AND APPLICATIONS
ACTIVITY DESCRIPTION

Purpose of the research group is to to treat various topics ranging from algebraic geometry and complex geometry to representation theory, problems in graph theory, algebraic and enumerative combinatorics and computational topics in commutative algebra. The applications vary in several directions among which image recognition, image processing, code theory, signal processing, neurosciences.

SKILL
  • mathematical analysis applied to mechanical systems
  • complex analysis techniques and transforms (Fourier, Laplace,…)
  • ordinary and partial differential equations
  • geometric analysis and Riemannian geometry
  • nonlinear diffusion
COMPONENTS OF THE GROUP
1 GAZZOLA Filippo PO
2 ABATANGELO Laura RTDB
3 ARIOLI Gianni PO
4 BIAGI Stefano RTDA
5 BOCCHI Edoardo Assegnista
6 BRAMANTI Marco PO
7 CATINO Giovanni PA
8 CIPRIANI Fabio PO
9 FALOCCHI Alessio RTDA
10 GARRIONE Maurizio RTDB
11 GRILLO Gabriele PO
12 MURATORI Matteo RTDB
13 NORIS Benedetta RTDB
14 PAVANI Raffaella PA
15 PUNZO Fabio PA
16 SOAVE Nicola RTDB
17 SPERONE MARTÌ Gianmarco Silvio RTDA
NON LINEAR ANALYSIS AND APPLICATIONS: MODELS AND METHODS
ACTIVITY DESCRIPTION
Existence and multiplicity\uniqueness results and qualitative properties of solutions of equations of elliptic, degenerate elliptic and mixed elliptic-hyperbolic types. Systems of semilinear elliptic equations with strongly competitive or noncooperative interaction. Inverse problems and stability. Variational and topological methods, critical points theory and bifurcation
KEY WORDS
Methods of global analysis on Riemannian manifolds. Maximum principles, sub/super-solutions. Variational and topological methods, critical points theory, bifurcation theory, Morse index theory. Blow-up techniques, monotonicity formulæ, Liouville-type theorems. Functional analysis and spectral analysis methods. Energy methods.
COMPONENTS OF THE GROUP
1 PIEROTTI Dario PA
2 BORRELLI William RTDB
3 CERUTTI Cristina PA
4 DI CRISTO Michele PA
5 GIULIANI Filippo RTDB
6 IANNELLI Angela RC
7 MONTICELLI Dario PA
8 VERZINI Gianmaria PA
NUMERICAL APPROXIMATION OF PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS
ACTIVITY DESCRIPTION

The group activity focuses on numerical modeling applied to problems arising from Engineering, Physics, Biomedicine, Earth Sciences. Large part of the activity is carried out within the MOX Laboratory (http://mox.polimi.it) and in particular the activity group numeth@mox (http://numeth.mox.polimi.it). From the applicative side, we deal with biomedical applications (http://bio.mox.polimi.it), computational geosciences (http://compgeo.mox.polimi.it), environmental applications and industrial mathematics (http://fluids.mox.polimi.it), electronic devices and bioelectronics (http://www1.mate.polimi.it/~ricsac/research.html).

KEY WORDS

Numerical analysis, Scientific computing and data processing, Applications of mathematics in science, Applications of mathematics in industry and society life

COMPONENTS OF THE GROUP
1 QUARTERONI Alfio PO
2 ANTONIETTI Paola Francesca PO
3 BONAVENTURA Luca PA
4 DE FALCO Carlo RTDB
5 DEDÈ Luca PA
6 FORMAGGIA Luca PO
7 MANZONI Andrea RTDB
8 MAZZIERI Ilario RTDB
9 MICHELETTI Stefano PA
10 MIGLIO Edie PA
11 PAROLINI Nicola PA
12 PEROTTO Simona PA
13 SACCO Riccardo PA
14 SCOTTI Anna RTDB
15 VERANI Marco PA
16 VERGARA Christian PA
17 ZUNINO Paolo PO
SCIENTIFIC DISSEMINATION AND INNOVATIVE LEARNING
ACTIVITY DESCRIPTION

The research activities are devoted to innovative didactics techniques and tools for the dissemination of mathematics (for instance MOOCs) and to the relationships of Mathematics with a variety of fields which include, for instance, architecture, art, theater, astronomy, cultural heritage, history and philosophy of science.

SKILL
The group is open to collaborations whith all subjects (public or also private, like publishing houses) interested in these fields.
COMPONENTS OF THE GROUP
1 MAGLI Giulio PO
2 BRUNETTO Domenico RTDB
3 EL SKAF Rawad RTDA
4 VALENTE GIOVANNI PA
QUANTITATIVE FINANCE
ACTIVITY DESCRIPTION

The Nicola Bruti Liberati Quantitative Finance Laboratory (QFinLab) is a high level center for training, research and collaboration with the industry in quantitative finance: asset management, risk management, derivative valuation. It is also active in the field of financial education, through the MOOC "Finance for All" and the activities on the website www.imparalafinanza.it, and in the field of new technologies and regulation analysis, with the dedicated website www.finriskalert.it

SKILL

The group has expertise in all areas of Quantitative Finance, which includes all applications of quantitative financial instruments (maths, statistics, computational methods) with applications ranging from valuation of derivatives to risk management, portfolio management, and financial product structuring.

COMPONENTS OF THE GROUP
1 BARUCCI Emilio PO
2 BAVIERA Roberto RTDB
3 GRASSETTI Francesca RTDA
4 MARAZZINA Daniele PA
MODERN MATHEMATICAL PHYSICS: FIELDS AND PARTICLES
ACTIVITY DESCRIPTION

Our research group investigates the mathematical features of quantum mechanics and quantum field theories as well as the theoretical aspects of non-equilibrium statistical mechanics.

Our main focus is on the derivation of rigorous mathematical results and their application to study complex physical phenomena ranging from meso- to microscopic scales.

The mathematical framework, within which our research is carried out, includes investigation tools like partial differential equations (PDE) and integro-differential equations, operator theory, nonlinear functional analysis.

Webpage: https://www.kinetic.mate.polimi.it

SKILL
  • Nonlinear models of quantum phenomena;
  • Superconductivity and superfluidity;
  • Few- and many-body Schrödinger operators;
  • Open quantum systems and decoherence;
  • Renormalization in quantum field theory;
  • Semi- and quasi-classical analysis in quantum field theory;
  • Quantum fields in black hole backgrounds;
  • Kinetic theory of rarefied gases and the Boltzmann equation;
  • Smoluchowski kinetic equation and its applications to biomedical research.
COMPONENTS OF THE GROUP
1 CORREGGI Michele PO
2 BELGIORNO Francesco domenico PA
3 FALCONI Marco RTDB
4 LORENZANI Silvia PA
GEOMETRY, ALGEBRA AND THEIR APPLICATIONS
ACTIVITY DESCRIPTION

Main research topics of the group refer to: algebra and theoretical computer science, commutative and computational algebra, complex and hypercomplex analysis, algebraic and enumerative combinatorics, geometric analysis, differential geometry, discrete mathematics, graph theory, representation theory.
Applications range in various directions including image reconstruction and recognition, discrete and geometric tomography, code theory, signal theory, neurosciences, topological data analysis.

Web page: https://www.geometry-algebra.polimi.it/en/

COMPONENTS OF THE GROUP
1 SABADINI Irene PO
2 CATINO Giovanni PO
3 D'ALÌ Alessio Maria RTDA
4 DULIO Paolo PA
5 GUMENYUK Pavel PA
6 HOCHENEGGER Andreas RTDB
7 LELLA Paolo PA
8 MOSENEDER Pierluigi PA
9 MUNARINI Emanuele PA
10 NOTARI Roberto PA
11 PINTON Stefano RTDB
12 RODARO Emanuele PA
13 SAMMARTANO Alessio RTDB
14 SCHLESINGER Enrico PA
15 SENTINELLI Paolo RTDA
OPTIMIZATION AND DECISION MAKING
ACTIVITY DESCRIPTION
The research interests of the groups are on the field of Optimization; in particular non cooperative and cooperative game theory both from a theoretical and a more applied point of view, and regularization procedures to solve inverse and machine learning problems
SKILL
The group can support consulting agencies within the area of complex decisions
COMPONENTS OF THE GROUP
1 LUCCHETTI Roberto PO
MATHEMATICAL PHYSICS MODELLING FOR ENGINEERING AND APPLIED SCIENCES
ACTIVITY DESCRIPTION

Mathematical modeling of complex multiphysics phenomena for applications in engineering in applied sciences, with particular focus on industry 4.0, space science and precision medicine.

SKILL

Modeling and numerical simulation of wave propagation, fluid dynamic instability and turbulence.
Applications of continuum mechanics in contexts of industrial relevance, with particular focus on developing data-driven models for industry 4.0 and space science.
Mathematical modeling of active soft matter, biological tissues with residual growth and tension, porous media, multiphase fluids and complex flows, rarefied gases, liquid crystals.
Development of predictive models of personalized medicine, of numerical simulation tools informed by clinical data and of machine learning methods to support medical decisions.

KEY WORDS

modelling, data driven methods, industry 4.0, space science, precision medicine

COMPONENTS OF THE GROUP
1 CIARLETTA Pasquale PO
2 BARBANTE Paolo RTI
3 MAGRI Marco RTDA
4 RICCOBELLI Davide RTDA
5 TURZI Stefano PA
6 VALDETTARO Lorenzo PA
7 VIANELLO Maurizio PO
MATHEMATICAL MODELS IN APPLIED SCIENCES. QUALITATIVE ANALYSIS
ACTIVITY DESCRIPTION
Mathematical analysis of evolution equations governing dissipative phenomena (e.g. fluid dynamics, hereditary processes, phase changes) with particular regard to well-posedness, regularity and longtime behavior of solutions. Inverse and control problems for differential equations.
SKILL
Knowledge of advanced theoretical tools to investigate the qualitative properties of mathematical models based on differential equations arising in several applied problems like, e.g., crack or inclusion identification, free boundaries, heat conduction in complex materials, phase separation in fluids, shape optimization, tumor growth, wave propagation in viscoelastic media.
COMPONENTS OF THE GROUP
1 GRASSELLI Maurizio PO
2 BERETTA Elena PA
3 COLLINI Tiziana RC
4 CONTI Monica PO
5 DELL'ORO Filippo RTDB
6 MARCHINI Elsa Maria PA
7 PATA Vittorino PO
8 SALSA Sandro PO
STOCHASTIC MODELS IN APPLIED SCIENCES
ACTIVITY DESCRIPTION

Analysis and modeling of random phenomena in physics, biology, finance, econometry. Stochastic optimization, filtering, control, backward stochastic equations. Bayesian inference. Quantum probability and information: quantum open systems, quantum optics applications, quantum uncertainty.

SKILL

Applications of models based on stochastic processes:

  • Optimal control in finite and infinite dimensions of Markovian and non-Markovian processes, of diffusive or pure-jump types; quadratic linear control. Applications to financial modeling.
  • Pricing and hedging of financial derivatives, in particular traded on Energy Markets.
  • Study of stochastic models of information/epidemic diffusion. This has a natural application, for instance, in the development of strategies to curb epidemics (vaccinations) or to favour the rapid dissemination of information.
  • Construction and statistical analysis of Cox-Markov models, construction of Bayesian semi-Markov processes, Bayesian survival analysis with applications to biological and seismic data. Bayesian econometric models of the regional population. Long experience in developing the theory and in applications of dynamical equations for quantum open systems and generators of quantum dynamical semigroups, the Schrödinger stochastic equation, quantum stochastic differential equations. Development of entropy techniques for information and uncertainty analysis in quantum systems that finds its natural application in the emerging field of quantum technologies.
COMPONENTS OF THE GROUP
1 FAGNOLA Franco PO
2 BARCHIELLI Alberto PO
3 BASSETTI Federico PA
4 BATTISTINI Egidio RC
5 CONFORTOLA Fulvia PA
6 DHAHRI Ameur PA
7 EPIFANI Ilenia PA
8 GREGORATTI Matteo PA
9 GUATTERI Giuseppina PA
10 LADELLI Lucia Maria PA
11 POLETTI Damiano Dottorando
12 SGARRA Carlo PA
13 TOIGO Alessandro PA
14 VERRI Maurizio PA
15 ZANELLA Margherita RTDA
16 ZUCCA Fabio PA
APPLIED STATISTICS
ACTIVITY DESCRIPTION

The group activity is focused on statistical models and methods applied to industrial problems or arising in biomedical sciences, geosciences and social sciences. Beside an intense theoretical research, also along the Bayesian approach, applied research is pursued within the MOX laboratory (http://mox.polimi.it) in the area Statistics@MOX (https://statistics.mox.polimi.it). Specific domains are those related to the analysis of complex and high dimensional data and to health analytics. The research focus in Bayesian statistics is on modelling and computational aspects, in particular on mixture models for clustering

KEY WORDS

Big data, statistical learning, functional data analysis, Bayesian statistics, data mining, generalized linear models with mixed effects, urn models for adaptive design of experiment, geostatistics, health care management.

COMPONENTS OF THE GROUP
1 SECCHI Piercesare PO
2 GUGLIELMI Alessandra PO
3 IEVA Francesca RTDB
4 MENAFOGLIO Alessandra RTDB
5 PAGANONI Anna Maria PO
6 SANGALLI Laura Maria PA
7 VANTINI Simone PA