Head of Dept:
Prof. Giulio Magli

Vice-Head of Dept:
Prof. Gabriele Grillo

Department Manager:
Dr.ssa Franca Di Censo

ALGEBRA, GEOMETRY AND THEIR 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.

KEY WORDS

Combinatorial and geometric semigroup theory; Automata and synchronisation; Algebraic structures defined by transducers and automata; Formal language theory; combinatorial analysis; theory of formal series enumerative combinatorics; umbral calculus; theory of graphs; algebraic graph theory; Generalised Graph Isomorphisms; Vertex-transitive Graphs and Digraphs; Distance in Graphs; compositions and integer sequences; discrete inverse problems for tomography; discrete geometry; image reconstruction; complex brain network; geometry of parameter spaces; classification of varieties and algebras with special properties; models described by polynomials in many variables; Computational algebraic geometry and commutative algebra; algebraic analysis and commutative algebra; Grobner bases.

COMPONENTS OF THE GROUP

1 | SABADINI Irene | PO |

2 | DULIO Paolo | RC |

3 | MONGODI Samuele | RTDA |

4 | MOSENEDER Pierluigi | PA |

5 | MUNARINI Emanuele | PA |

6 | NOTARI Roberto | PA |

7 | RODARO Emanuele | RTDB |

8 | SCHLESINGER Enrico | PA |

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. 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

- 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 | COLOMBO Fabrizio | PO |

3 | FRAGALÀ Ilaria | PO |

4 | LAENG Enrico | PA |

5 | MALUTA Elisabetta | PA |

6 | MARCHIONNA Clelia | PA |

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 | ARIOLI Gianni | PO |

3 | BRAMANTI Marco | PO |

4 | CATINO Giovanni | PA |

5 | CIPRIANI Fabio | PO |

6 | GARRIONE Maurizio | RTDB |

7 | GRILLO Gabriele | PO |

8 | MURATORI Matteo | RTDB |

9 | PAVANI Raffaella | PA |

10 | PUNZO Fabio | PA |

11 | SOAVE Nicola | RTDB |

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 | CERUTTI Cristina | PA |

3 | DI CRISTO Michele | PA |

4 | IANNELLI Angela | RC |

5 | MONTICELLI Dario | PA |

6 | 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 | RTDA |

3 | MAGNAGHI Paola | RTI |

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 |

MATHEMATICAL PHYSICS

ACTIVITY DESCRIPTION

Mathematical modelling of complex physical phenomena: growth in biological tissues, complex fluids and flows, rarefied gases. Liquid crystals and soft matter. Elasticity theory, classical planetary mechanics and black hole theory are also investigated.

SKILL

Modelling and numerical simulation of wave propagation, fluid dynamics instabilities and turbulence. Applications of gas kinetic theory (Boltzmann equation) to micro- and nano-devices. Mathematical modelling of transport and diffusion properties in porous media and of tumor growth in living matter. Applications of continuum mechanics to morpho-elasticity and other mechanical contexts. Modelling of residual stresses and of active response in soft matter. Relationship between fibers and matrix in living tissues. Groups and symmetries in soft matter. Regularization of the Kepler problem in classical mechanics and quantum fields in black hole backgrounds.

COMPONENTS OF THE GROUP

1 | VIANELLO Maurizio | PO |

2 | BARBANTE Paolo | RC |

3 | BELGIORNO Francesco Domenico | PA |

4 | CIARLETTA Pasquale | PA |

5 | LORENZANI Silvia | PA |

6 | TURZI Stefano | RTDB |

7 | VALDETTARO Lorenzo | PA |

8 | VIVARELLI Maria Dina | PA |

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 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 | BARCHIELLI Alberto | PO |

2 | BASSETTI Federico | PA |

3 | BATTISTINI Egidio | RC |

4 | CONFORTOLA Fulvia | PA |

5 | DHAHRI Ameur | PA |

6 | EPIFANI Ilenia | PA |

7 | FAGNOLA Franco | PO |

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 | ZUCCA Fabio | RC |

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, even 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 (https://statistics.mox.polimi.it/research/high-dimensional-and-complex-data/), health care management and clinical biostatistics (https://statistics.mox.polimi.it/research/health-care-assessment-clinical-biostatistics/), urn models for adaptive design of experiments (https://statistics.mox.polimi.it/research/urn-models-for-response-adaptive-designs/). The research focus in Bayesian statistics is on modelling and computational aspects, in particular on mixture models for clustering (http://www1.mate.polimi.it/~guglielmi/#two)

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 |