• Topology1
    Topology optimization of structures
    and metamaterials

    (courtesy of Proff. Simona Perotto, Stefano Micheletti, Dr. Nicola Ferro)
    Topology optimization of structures<br>and metamaterials
    Topology optimization of structures
    and metamaterials
    (courtesy of Proff. Simona Perotto, Stefano Micheletti, Dr. Nicola Ferro)

    Additive Manufacturing has changed the way to conceive the production of structures and materials. Topology optimization offers us a rigorous tool for increasingly efficient and new designs

  • q500-4-low
    Numerical simulation of blood flow in the heart
    (courtesy of Prof. Alfio Quarteroni)
    Numerical simulation of blood flow in the heart
    Numerical simulation of blood flow in the heart
    (courtesy of Prof. Alfio Quarteroni)

    iHEART, which refers to “integrated heart model for the simulation of the cardiac function”, represents one of the first attempts in the world to create a complete mathematical model of the human heart.

  • brain1
    Statistical analysis of high-dimensional
    neuroimaging data

    (Courtesy of Prof. Laura Sangalli)
    Statistical analysis of high-dimensional<br>neuroimaging data
    Statistical analysis of high-dimensional
    neuroimaging data
    (Courtesy of Prof. Laura Sangalli)

    Advanced statistical techniques enable the study of high-dimensional neuroimaging signals associated with neuronal activity and connectivity, complying with the complicated morphology of the brain

  • zunino
    Numerical simulation of microcirculation
    and tissue microenvironment

    (courtesy of Prof. Paolo Zunino)
    Numerical simulation of microcirculation<br>and tissue microenvironment
    Numerical simulation of microcirculation
    and tissue microenvironment
    (courtesy of Prof. Paolo Zunino)

    Computational models describe the delivery of oxygen to the tissue microenvironment of a tumor, which in turn influences the efficacy of radiotherapy and the corresponding cell survival fraction.

  • ponte
    Vortex shedding around
    the deck of a bridge

    (courtesy of Proff. Denis Bonheure, Filippo Gazzola, Gianmarco Sperone)
    Vortex shedding around<br>the deck of a bridge
    Vortex shedding around
    the deck of a bridge
    (courtesy of Proff. Denis Bonheure, Filippo Gazzola, Gianmarco Sperone)

    The origin of instability in bridges: CFD simulation of vortices around the deck for a fluid obeying to the Navier-Stokes equations (courtesy of Proff. Denis Bonheure, Filippo Gazzola, Gianmarco Sperone).

  • terremoto
    Numerical simulation of
    seismic events

    (courtesy of Prof. Paola Antonietti)
    Numerical simulation of<br>seismic events
    Numerical simulation of
    seismic events
    (courtesy of Prof. Paola Antonietti)

    High performance numerical simulations for the reliable prediction of near-fault ground motions and seismic response of strategic structures in complex 3D scenarios.

  • estrusion
    Numerical simulation of polymer extrusion
    (courtesy of Pof. Marco Verani)
    Numerical simulation of polymer extrusion
    Numerical simulation of polymer extrusion
    (courtesy of Pof. Marco Verani)

    Numerical simulations of complex fluids in moving domains is of crucial importance to improve the performance of the extrusion process in several industrial applications.

General information

The Department of Mathematics of the Politecnico di Milano is hosting a PhD program in Mathematical Models and Methods in Engineering, aiming at training high level researchers in advanced areas of Pure and Applied Mathematics. The teaching activities include a broad range of possibilities designed for the PhD program. As a successful approach to practical applications depends on a deep understanding of real-world phenomena and knowledge of mathematical tools for their description and design, both modelling, methodological and theoretical aspects are included. Courses are offered in various areas of mathematics, and may vary every year.

Geometrindi e Matematindi (Luigi Serafini 2002)

Geometrindi e Matematindi (Luigi Serafini 2002)

Numerical simulation of blood flow in the heart (courtesy of Prof. Alfio Quarteroni)

Numerical simulation of blood flow in the heart (courtesy of Prof. Alfio Quarteroni)

Objectives

The development of advanced technologies in Science and Engineering brings an increasing demand of advanced mathematical theories and methods, which in turn fosters the demand for education and training of skilled mathematicians in pure and applied research. The main scope of the Ph.D. course “Mathematical Models and Methods in Engineering” is to train high-level researchers in various fields of pure and applied mathematics.

Professional Opportunities

Expected professional placements for Ph.D. doctorates are: academic research in Italian or International Universities and Research Institutions, R & D divisions of private companies, study and research centers of public Agencies, financial and insurance Institutions.

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
    logo matematica
    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
    logo matematica
    • 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
    logo matematica
    • 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
    logo matematica
    • 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
    logo matematica
    • 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
    logo matematica
    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
    logo matematica
    • 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