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 VECCHI Eugenio 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 BRAMANTI Marco PO
6 CATINO Giovanni PA
7 CIPRIANI Fabio PO
8 GARRIONE Maurizio RTDB
9 GRILLO Gabriele PO
10 MURATORI Matteo RTDB
11 NORIS Benedetta RTDB
12 PAVANI Raffaella PA
13 PUNZO Fabio PA
14 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
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 DULIO Paolo PA
4 GUMENYUK Pavel PA
5 HOCHENEGGER Andreas RTDB
6 LELLA Paolo PA
7 MOSENEDER Pierluigi PA
8 MUNARINI Emanuele PA
9 NOTARI Roberto PA
10 PINTON Stefano RTDA
11 RODARO Emanuele PA
12 SAMMARTANO Alessio RTDB
13 SCHLESINGER Enrico PA
14 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 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
Upcoming events
  • dec 13 mon 2021

    Seminar
    Riccardo Adami, Ground states for the two-dimensional NLS in the presence of point interactions,  12-13-2021, 14:00
    logo matematica
    • Seminar
    • Riccardo Adami
    • Politecnico di Torino
    • Ground states for the two-dimensional NLS in the presence of point interactions
    • Monday, 13 December 2021 at 14:00
    • Sala Consiglio - Piano VII
    • Abstract
      We prove the existence of ground states, i.e. minimizers of the energy at fixed mass, for the focusing, subcritical Nonlinear Schroedinger equation in two dimensions, with a linear point interaction, or defect. Ground states turn out to be positive up to a phase, and to show a logaritmico singularity at the defect. The analogous problem has been widely treated in the one dimensional setting, including the case of graphs. The two dimensional version is more complicated because of the structure of the energy space, that is larger than the standard one. This result opens the way to the study of nonlinear hybrids. This is a joint work with Filippo Boni, Raffaele Carlone, and Lorenzo Tentarelli.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • dec 14 tue 2021

    MOX Seminar
    Mattia Serra, A mechanochemical instability drives vertebrate gastrulation,  12-14-2021, 14:30
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    MOX
    MOX bio

    • MOX Seminar
    • Mattia Serra
    • University of California, San Diego
    • A mechanochemical instability drives vertebrate gastrulation
    • Tuesday, 14 December 2021 at 14:30
    • Live: Aula Consiglio, VII piano, Dip. di Matematica
      Online: mox.polimi.it/mox-seminars/?id_evento=2101
    • Abstract
      Gastrulation is a critical event in vertebrate morphogenesis, characterized by coordinated large-scale multi-cellular movements. One grand challenge in modern biology is understanding how spatio-temporal morphological structures emerge from cellular processes in a developing organism and vary across vertebrates. We derive a theoretical framework that couples tissue flows, stress-dependent myosin activity, and actomyosin cable orientation. Our model, consisting of a set of nonlinear coupled PDEs, predicts the onset and development of observed experimental patterns of wild-type and perturbations of chick gastrulation as a spontaneous instability of a uniform state. We use analysis and numerics to show how our model recapitulates the phase space of gastrulation morphologies seen across vertebrates, consistent with experiments. Altogether, this suggests that early embryonic self-organization follows from a minimal predictive theory of active mechano-sensitive flows. www.biorxiv.org/content/10.1101/2021.10.03.462928v2

      Contatto: pasquale.ciarletta@polimi.it
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • dec 15 wed 2021

    Seminar
    Francesco Nappo, Modelli nella scienza e nella pedagogia scientifica: il caso di J. Clerk Maxwell,  12-15-2021, 15:00
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    • Seminar
    • Francesco Nappo
    • Politecnico di Milano
    • Modelli nella scienza e nella pedagogia scientifica: il caso di J. Clerk Maxwell
    • Wednesday, 15 December 2021 at 15:00
    • online tiny.cc/fds22webex
    • Abstract
      Utilizzeremo il caso delle teorie elettromagnetiche di James Clerk Maxwell per illustrare il ruolo dei modelli e dell' analogia nella produzione di nuova conoscenza fisica.
      In particolare, discuteremo di come il modello dei vortici nel suo articolo 'On Physical Lines of Forces' (1861-62) e l'utilizzo del ragionamento analogico abbiano avuto un ruolo centrale nella formulazione delle famose equazioni elettromagnetiche.
      Come evidenziato da diversi studi, descrivere gli aspetti storici ed epistemologici di episodi centrali nella storia della scienza è importante dal punto di vista didattico, dal momento che contribuisce ad una migliore comprensione da parte degli studenti del ruolo chiave dei modelli nella ricerca scientifica e allo sviluppo di competenze modellistiche.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • dec 15 wed 2021

    Seminar
    Irina Markina, From Clifford algebras to Heisenberg type Lie algebras,  12-15-2021, 18:00
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    • Seminar
    • Irina Markina
    • University of Bergen, Norway
    • From Clifford algebras to Heisenberg type Lie algebras
    • Wednesday, 15 December 2021 at 18:00
    • On line
    • Abstract
      As it is well known, the Clifford algebras have numerous applications. In the present talk, we will explain how the Clifford algebras and their representation can build two-step nilpotent Lie algebras. They received the name Heisenberg type Lie algebras, due to the fact that the classical Heisenberg algebra is the simplest example in this construction.

      A special class of Heisenberg type Lie algebras was introduced by A. Kaplan in 1980 to study hypoelliptic partial differential operators and their fundamental solutions. The Heisenberg type Lie algebras admit rational structural constants, that lead to the existence of lattices on the corresponding Lie groups according to the Malcev theorem. The factor of Heisenberg type Lie groups by the lattices gives rise to a chain of examples of nilmanifolds that are isospectral but non-diffeomorphic.

      In the talk, we will explain the construction of the Heisenberg type Lie algebras and give examples. We also will discuss the classification of the constructed Lie algebras and their group of automorphisms.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jan 12 wed 2022

    Seminar
    Andrea Pascucci, Didattica della Probabilità: idee e applicazioni,  01-12-2022, 15:00
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    • Seminar
    • Andrea Pascucci
    • Università di Bologna
    • Didattica della Probabilità: idee e applicazioni
    • Wednesday, 12 January 2022 at 15:00
    • online tiny.cc/fds22webex
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jan 26 wed 2022

    Seminar
    Flavia Mammana & Eugenia Taranto, Percorsi di matematica all'aperto con MathCityMap,  01-26-2022, 15:00
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    • Seminar
    • Flavia Mammana & Eugenia Taranto
    • Università di Catania
    • Percorsi di matematica all'aperto con MathCityMap
    • Wednesday, 26 January 2022 at 15:00
    • online tiny.cc/fds22webex
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jan 27 thu 2022

    MOX Seminar
    Alfio Borzi, The Pontryagin maximum principle and the training of Runge-Kutta neural networks,  01-27-2022, 11:00
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    MOX
    MOX Numeth

    • MOX Seminar
    • Alfio Borzi
    • Università di Wuerzburg
    • The Pontryagin maximum principle and the training of Runge-Kutta neural networks
    • Thursday, 27 January 2022 at 11:00
    • Live: Aula Consiglio - Dipartimento di Matematica - Politecnico di Milano
      Online: mox.polimi.it/mox-seminars/?id_evento=2109
    • Abstract
      In residual neural networks and related NN architectures, supervised learning problems can be reformulated as optimal control problems governed by discrete-in-time nonlinear evolution models.

      This talk is devoted to the analysis and solution of these problems in the framework of a discrete version of the Pontryagin maximum principle and of neural networks with Runge-Kutta (RK) structure. In particular, a sequential quadratic Hamiltonian (SQH) method for solving the corresponding supervised learning problems is presented. Convergence properties of the SQH scheme are investigated theoretically and numerically, and results of numerical experiments are presented that demonstrate the advantageous performance of the SQH learning algorithm.

      Contatto: marco.verani@polimi.it
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • feb 09 wed 2022

    Seminar
    Fabio Zucca, Impariamo a contare: introduzione all'analisi combinatoria,  02-09-2022, 15:00
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    • Seminar
    • Fabio Zucca
    • Politecnico di Milano
    • Impariamo a contare: introduzione all'analisi combinatoria
    • Wednesday, 9 February 2022 at 15:00
    • online tiny.cc/fds22webex
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568