• 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
  • oct 18 mon 2021

    Seminar
    Paolo Piovano, Analytical validation of variational models for epitaxially strained thin films,  10-18-2021, 14:15
    logo matematica
    • Seminar
    • Paolo Piovano
    • Politecnico di Milano
    • Analytical validation of variational models for epitaxially strained thin films
    • Monday, 18 October 2021 at 14:15
    • polimi-it.zoom.us/j/88014306666?pwd=Vi8rejZPMEFDK0YyUGNJb1pwV25Cdz09
    • Abstract
      The derivation of variational models describing the epitaxial growth of thin films in the framework of the theory of Stress-Driven Rearrangement Instabilities (SDRI) will be presented, and the state of the art of the mathematical results described. By working in the context of both continuum and molecular mechanics, not only free boundary problems, but also atomistic models will be considered, and the discrete-to-continuum passage rigorously investigated in the intent to also provide a microscopical justification of the theory. An overview of the mathematical results achieved through the years with various co-authors for the existence, regularity and evolution of the solutions will be presented.
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • oct 19 tue 2021

    MOX Seminar
    Gabriele Ciaramella, On a greedy algorithm for the Hamiltonian identification,  10-19-2021, 11:00
    logo matematica
    MOX
    MOX Numeth

    • MOX Seminar
    • Gabriele Ciaramella
    • MOX, Dipartimento di Matematica, Politecnico di Milano
    • On a greedy algorithm for the Hamiltonian identification
    • Tuesday, 19 October 2021 at 11:00
    • Live: Aula Saleri, MOX - Dipartimento di Matematica - Politecnico di Milano
      Online: mox.polimi.it/elenco-seminari/?id_evento=2085&t=763721
    • Abstract
      The identification of Hamiltonian operators plays a fundamental role in fields like quantum physics, quantum chemistry and nuclear magnetic resonance. The term Hamiltonian identification often refers to two distinct problems. On the one hand, it can indicate the inverse problem associated with the identification of a Hamiltonian operator obtained by a numerical fitting of simulated experimental data. On the other hand, it can refer to both the problem of designing experimental parameters (input control functions) allowing a tailored production of laboratory data and the subsequent inverse identification problem.
      In this talk, a novel computational greedy-type approach for design of control functions will be presented and analyzed. This strategy is based on an offline/online decomposition of the
      reconstruction process. In the offline phase, a family of control functions is built iteratively in a greedy manner to maximize the distinguishability of the system. This phase exploits only the theoretical quantum model, without any use of laboratory information. The computed control functions are experimentally implemented in the online phase to produce laboratory data, which are in turn used to define and solve an identification inverse problem.
      The convergence analysis reveals the strong dependence of the performance of the greedy strategy on the observability and controllability of the system and allows us to introduce a new and more robust optimized greedy strategy whose efficiency is demonstrated by numerical experiments.
      Contatto: paola.antonietti@polimi.it
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • oct 19 tue 2021

    Seminar
    Paolo Sentinelli, Stratificazioni di incidenza,  10-19-2021, 15:00 precise
    logo matematica
    • Seminar
    • Paolo Sentinelli
    • Politecnico di Milano
    • Stratificazioni di incidenza
    • Tuesday, 19 October 2021 at 15:00 right
    • Aula seminari MOX VI piano, online su pagina webex di Roberto Notari
    • Abstract
      Introdurremo la nozione di stratificazione di incidenza di una varietà proiettiva.
      Esempi classici di strati di incidenza sono le varietà di Schubert e gli strati matroidali delle grassmanniane, le varietà di Schubert e gli strati matroidali nelle varietà delle bandiere. Nei casi in cui valga una proprietà di massimalità matroidale, la stratificazione di incidenza dà un insieme di generatori del gruppo di Chow della varietà.

      We introduce the notion of incidence stratification of a projective variety. Classical examples of incidence strata are Schubert varieties and matroidal strata in Grassmannians, Schubert varieties and matroidal strata in flag varieties. In case a matroidal maximality property holds, the incidence stratification gives a set of generators for the Chow group of the variety.
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • oct 20 wed 2021

    MOX Seminar
    Karel Hron, Orthogonal decomposition and functional data analysis of bivariate densities in Bayes spaces,  10-20-2021, 11:30
    logo matematica
    MOX
    MOX Statistics

    • MOX Seminar
    • Karel Hron
    • Palacky University - Olomouc
    • Orthogonal decomposition and functional data analysis of bivariate densities in Bayes spaces
    • Wednesday, 20 October 2021 at 11:30
    • Live: Room B.6.1, Building 14, Politecnico di Milano
      Online: mox.polimi.it/elenco-seminari/?id_evento=2083&t=763721
    • Abstract
      A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces will be presented. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised definitions of marginal densities and the latter capturing the dependence between the two random variables being studied. The developed framework opens new perspectives for dependence modelling (which is commonly performed through copulas), and allows for the analysis of dataset of bivariate densities, in a Functional Data Analysis perspective.
      Contact: alessandra.menafoglio@polimi.it
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • oct 27 wed 2021

    WorkShop
    Esperienze a confronto in tema di educazione finanziaria
    10/27/2021
    logo matematica
    • WORKSHOP
    • Esperienze a confronto in tema di educazione finanziaria
    • organizers
      Gruppo QFinLab
    • Per fronteggiare efficacemente i cambiamenti sociali, economici, ambientali e demografici che si susseguono è necessaria la capacità di prendere decisioni consapevoli e responsabili in ambito economico e finanziario. A seguito della crisi finanziaria, c’è oramai ampia evidenza che l’alfabetizzazione finanziaria delle persone rappresenti un ingrediente fondamentale per garantire la stabilità economica e finanziaria. Tendenze di lungo periodo, quali il processo di digitalizzazione e l’invecchiamento demografico, hanno implicazioni dirette nella vita dei singoli che sono obbligati a utilizzare nuovi sistemi di pagamento e a fronteggiare nuovi scenari previdenziali. Eventi imprevisti come la pandemia Covid-19 hanno aggiunto criticità sul fronte finanziario che hanno colpito soprattutto le persone con un basso livello di reddito e di scolarizzazione. Come affrontare queste sfide? Come promuovere tra giovani e adulti le conoscenze finanziarie, assicurative e previdenziali che garantiscono di compiere scelte finanziarie in modo consapevole? La conferenza Esperienze a confronto in tema di educazione finanziaria raccoglie le testimonianze più significative nell’ambito dell’educazione finanziaria (adulti e studenti) con l’obiettivo di sviluppare un’approfondita discussione sui nodi del passato, le buone pratiche da replicare e le sfide del futuro al fine di progettare iniziative sempre più efficaci. Interverranno: Tommaso Agasisti (Politecnico di Milano) Valutare gli interventi di educazione finanziaria – evidenze da alcuni recenti esperimenti in scuole ed università Giovanna Boggio Robutti (FEduF) Coniugare l’educazione finanziaria con cittadinanza economica e sostenibilità: l’esperienza della FEduF Riccardo De Bonis (Banca d’Italia) Le iniziative della Banca d’Italia nelle scuole: che cosa ha funzionato, che cosa dobbiamo migliorare Nadia Linciano (Consob) Sperimentazione nell’educazione finanziaria di giovani e adulti: l’esperienza della Consob. Annamaria Lusardi (The George Washington University) Quale è l’impatto dell’educazione finanziaria? L’evidenza empirica in 33 paesi. Daniele Marazzina (Politecnico di Milano) L’esperienza Edufin@polimi: progetti ed evidenze nei primi cinque anni di attività Giovanna Paladino (Intesa San Paolo) Edutainment e alfabetizzazione finanziaria: l’esperienza decennale del Museo del Risparmio Claudia Segre (Global Thinking Foundation) Donne e Ragazze resilienti: responsabili del cambiamento
    • Wednesday, 27 October 2021 - Wednesday, 27 October 2021
      Online
    Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
  • oct 27 wed 2021

    Seminar
    Ali Guzman Adan, The Dirac delta distribution and inversion formulas for the Radon transform in superspace,  10-27-2021, 17:00
    logo matematica
    • Seminar
    • Ali Guzman Adan
    • University of Ghent
    • The Dirac delta distribution and inversion formulas for the Radon transform in superspace
    • Wednesday, 27 October 2021 at 17:00
    • On line (seguirà link)
    • Abstract
      In this talk, we approach the problem of inverting the Radon transform in superspace from two different perspectives. The first one relies on the decomposition into plane waves of the super Dirac Delta distribution, provided that the superdimension is not odd and negative. Such a decomposition is obtained by adopting the point of view of hyperfunctions, namely by using the fact that the Dirac delta is a suitable boundary value of the super Cauchy kernel. In the cases of negative and even superdimension, the obtained formulas no longer resemble the structure of the classical plane wave decompositions in m real dimensions. In turn, the explicit inversion formulas obtained for the super Radon transform in these cases show important differences with the classical case.

      On the other hand, we show how to invert the super Radon transform using the classical approach, i.e. by composing the dual Radon transform with a certain power of the super Laplace operator. This approach yields a unified inversion formula that is valid for all possible integer values of the superdimension. The proof of this result comes along with the study of fractional powers of the super Laplacian, their fundamental solutions, and the plane wave decompositions of super Riesz kernels. This talk is based on joint work with Irene Sabadini and Frank Sommen.
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • nov 15 mon 2021

    Seminar
    Kestutis Cesnavicius, The perfectoid approach to purity questions,  11-15-2021, 16:00
    logo matematica
    • Seminar
    • Kestutis Cesnavicius
    • Institut de Mathématique d'Orsay, Université Paris-Saclay
    • The perfectoid approach to purity questions
    • Monday, 15 November 2021 at 16:00
    • Sala di Rappresentanza, Via C. Saldini 50, Milano e ON LINE
    • Abstract
      Purity in arithmetic algebraic geometry is the phenomenon of certain invariants of algebraic varieties being insensitive to removing closed subvarieties of sufficiently large codimension, the Hartogs' extension principle being the basic example. The most delicate case of such results is in mixed characteristic (0, p), in which a new approach based on perfectoid rings has recently been introduced. I will overview it and discuss the results that it has yielded so far.
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568