• 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
  • jun 14 mon 2021

    Seminar
    Vincent Martinez, On unique ergodicity, regularity, and mixing for the weakly-damped stochastic KdV equation.,  06-14-2021, 17:30 precise
    logo matematica
    • Seminar
    • Vincent Martinez
    • CUNY Hunter College
    • On unique ergodicity, regularity, and mixing for the weakly-damped stochastic KdV equation.
    • Monday, 14 June 2021 at 17:30 right
    • us02web.zoom.us/j/85740643260?pwd=SzFjTXo0bWE3YjI3VWo0b3krT09kdz09
    • Abstract
      We discuss the existence, uniqueness, and regularity of invariant measures for the damped-driven stochastic Korteweg-de Vries equation, where the noise is additive and sufficiently non-degenerate. It is shown that a simple, but versatile control strategy, typically employed to establish exponential mixing for strongly dissipative systems such as the 2D Navier-Stokes equations, can nevertheless be applied in this weakly dissipative setting to establish elementary proofs of both unique ergodicity, albeit without mixing rates, as well as regularity of the support of the invariant measure. Under the assumption of large damping, however, a one-force, one-solution principle is established, from which we are able to deduce the existence of a spectral gap with respect to a Wasserstein distance-like function.
    • 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

  • jun 16 wed 2021

    Seminar
    Daniel Alpay, Discrete analytic functions and Schur analysis,  06-16-2021, 17:00
    logo matematica
    • Seminar
    • Daniel Alpay
    • Chapman University
    • Discrete analytic functions and Schur analysis
    • Wednesday, 16 June 2021 at 17:00
    • On line
    • Abstract
      We first review both the theory of discrete analytic functions and the main features of Schur analysis (a collection of problems pertaining to functions analytic and contractive in the open unit disk, and with a wide range of applications). Then, we present new connections between the theory of discrete analytic functions and Schur analysis. This allows us to define a new class of problems pertaining to discrete analytic functions.

      References:

      D. Alpay, P. Jorgensen, R. Seager, and D. Volok. On discrete analytic functions: Products, Rational Functions, and Reproducing Kernels. Journal of Applied Mathematics and Computing. Volume 41, Issue 1 (2013), Page 393-426.

      D. Alpay and D. Volok, Discrete analytic functions and Schur analysis. Preprint, 2021.

    • 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

  • jun 21 mon 2021

    Seminar
    Jacopo De Simoi, Dynamical rigidity of convex billiards,  06-21-2021, 17:00
    logo matematica
    • Seminar
    • Jacopo De Simoi
    • University of Toronto
    • Dynamical rigidity of convex billiards
    • Monday, 21 June 2021 at 17:00
    • zoom.us/j/91544493126?pwd=cHVlNEFkZ1lHWjNONG9kWHdoaGwxQT09
    • Abstract
      Convex billiards are a classical topic in conservative dynamics. Typically, their dynamics is qualitatively very intricate, since it showcases a coexistence of hyperbolic dynamics and KAM phenomena. Understanding long-term statistical properties of the dynamics with the current technology is essentially an intractable problem.

      Here I venture in the opposite direction and I will discuss dynamical inverse problems: how much geometrical information can be extracted from the dynamics?

      More precisely: what can be deduced about the billiard table if one knows the lengths of all periodic orbits? The quantum version of this question has been famously stated as "Can one hear the shape of a drum?"

      In this talk I will review the latest results and describe the next steps in this direction. This is a joint project with Vadim Kaloshin.
    • 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

  • jul 01 thu 2021

    jul 03 sat 2021

    WorkShop
    Modelling the cardiac function
    07/01/2021 - 07/03/2021
    logo matematica
    • WORKSHOP
    • MCF2021
      Modelling the cardiac function
    • organizers
      Alfio Quarteroni (chair) - Luca Dede' - Andrea Manzoni - Christian Vergara - Paolo Zunino
    • This Congress aims at focusing on the state of the art in the mathematical modelling and numerical simulation of the cardiac function and its clinical applications. This event will host plenary lectures from distinguished scientists as well as contributed talks. The event will take place online. This is the fifth Conference of the series MPF - Modelling the Physiological Flows and is organized by MOX - Politecnico di Milano, with the support of the EU ERC-ADG - Advanced Grant iHEART Project ID: 740132 - iheart.polimi.it
    • Thursday, 1 July 2021 - Saturday, 3 July 2021
      Online event: register at iheart.polimi.it/mcf2021
    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