• 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
  • 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
    • Abstract
      I Math Trails, percorsi di matematica, permettono agli studenti di scoprire la matematica al di fuori dell’ambiente scolastico, risolvendo problemi creati su oggetti reali misurando, contando, modellizzando. Proposti in Australia negli anni ’80 del secolo scorso, inizialmente in occasioni ricreative e poi in ambienti didattici, sono stati oggetto di attenzione da parte di studiosi di didattica della matematica. Nel 2016 nasce il sistema MathCityMap (mathcitymap.eu/it/) che permette di preparare e organizzare percorsi di matematica mediante strumenti digitali.
      MathCityMap, ideato dal gruppo di didattica della matematica del Dipartimento di Matematica e Informatica della Goethe-Universitaet di Francoforte, sotto la guida del Prof. Matthias Ludwig, è un sistema che si compone di un portale web e di una app per smartphone. Il portale contiene informazioni sul sistema stesso, percorsi di matematica già pronti e collocati su tutto il continente (e non solo) e permette agli insegnanti di creare nuovi percorsi, adattandoli alle proprie esigenze. L’applicazione per smartphone consente all’utente, generalmente uno studente, di eseguire il percorso.
      Durante il seminario verrà illustrato il sistema MathCityMap (portale e app), verranno messe in evidenza le ricadute didattiche di attività che si avvalgono di tale sistema e si proporrà un Math Trail da remoto.
      Si consiglia di scaricare, prima del seminario, l’applicazione gratuita “MathCityMap” sul proprio smartphone (dal proprio PlayStore).
    • 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

  • feb 10 thu 2022

    MOX Colloquia
    Ron Kenett, Topics on Digital twins: Hybrid modeling, befitting cross validation and dynamical systems,  02-10-2022, 14:00
    logo matematica
    MOX
    MOX Fluids
    MOX Numeth
    MOX Statistics

    • MOX Colloquia
    • Ron Kenett
    • The KPA Group, Raanana and the Samuel Neaman Institute, Technion, Israel
    • Topics on Digital twins: Hybrid modeling, befitting cross validation and dynamical systems
    • Thursday, 10 February 2022 at 14:00
    • Online seminar: mox.polimi.it/mox-seminars/?id_evento=2120
    • Abstract
      The talk is designed to provide an introduction to digital twins, mainly in the context of system and industrial applications. Three other topics will be covered which provide directions for further research. These include: i) hybrid modeling, ii) befitting cross validation and iii) dynamical systems.

      Hybrid modeling combines engineering based mechanical models with phenomenological models: Typically, mechanistic models are developed from first principles based on some information about a system of interest. This is in contrast to phenomenological models, which are data-driven in nature, viewing the system as a black box. Hybrid modeling is the integration of the two modeling approaches. A second topic relates to context dependent cross validation of predictive analytic models. Specifically, a methodology labeled befitting cross validation (BCV) will be presented. BCV is particularly suited to validating digital twin models.

      A third topic to be covered is modeling dynamical systems with deterministic ordinary/partial differential equations. Mathematical and statistical models permit to measure and predict the state of a process in time and space, and enable the development of monitoring, diagnostic and prognostic capabilities for process control purposes, as well as for efficiency and predictive maintenance implementation. These are the main analytic capabilities of digital twins.

      Contatto: piercesare.secchi@polimi.it
    • Ron Kenett

      Ron Kenett

      Professor Ron Kenett is Chairman of the KPA Group, Israel, Chairman of the Data Science Society at AEAI, Senior Research Fellow at the Samuel Neaman Institute, Technion, Haifa, Israel and Research Professor at the University of Turin, Italy. Past president of the Israel Statistical Association and the European Network for Business and Industrial Statistics. Authored and co-authored over 250 papers and 16 books on applied statistics topics. Awarded the 2013 Greenfield Medal by the Royal Statistical Society and, in 2018, the Box Medal by the European Network for Business and Industrial Statistics. PhD in Mathematics from the Weizmann Institute under supervision of Sam Karlin and BSc. in Mathematics, with fist class honors,from Imperial College. Ron is emphasizing the role of information quality as a main objective of statistical analysis
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • feb 16 wed 2022

    Course
    Pomeriggio di formazione - sorgenti e sviluppo di un calcolo infinitesimale senza infinitesimi. una nuova proposta didattica
    02/16/2022
    logo matematica
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • mar 14 mon 2022

    WorkShop
    Piday 2022
    03/14/2022
    logo matematica
    • WORKSHOP
    • Piday 2022
    • organizers
      Laboratorio FDS
    • In occasione del PiDay e della Giornata Internazionale della Matematica, il Laboratorio Effediesse del Politecnico di Milano promuove un evento, con la finalità di avvicinare i giovani delle scuole secondarie alla matematica: si tratta di una gara matematica dal titolo “Pi greco e la misura delle figure geometriche”. La gara è rivolta a tutti gli studenti delle scuole secondarie (di primo e secondo grado) e consiste nella preparazione di un elaborato creativo multimediale (video) sul tema “Le misure delle figure geometriche: equivalenze, rapporti, approssimazioni”. Per partecipare è necessario pre-iscriversi entro il 23 Gennaio 2022 compilando il seguente form https://forms.gle/gBn7D231QcBxqw4w5 L'evento conclusivo si terrà online il giorno del PiDay2022, quindi proprio il 14 Marzo 2022 online.
    • Monday, 14 March 2022 - Monday, 14 March 2022
      Online
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • mar 14 mon 2022

    Seminar
    Laboratorio FDS, PiDay 2022,  03-14-2022, 09:00
    logo matematica
    • Seminar
    • Laboratorio FDS
    • Politecnico di Milano
    • PiDay 2022
    • Monday, 14 March 2022 at 09:00
    • Online
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568