• Topology1
    Topology optimization of structures
    and metamaterials
    (courtesy of Proff. Simona Perotto, Stefano Micheletti, Dr. Nicola Ferro)
    ...more
    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

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.

Today's events

  • apr 03 thu 2025

    jul 10 thu 2025

    		WorkShop
    Mathematics colloquium of milano: inaugural cycle
    04/03/2025 - 07/10/2025
    logo matematica
    • WORKSHOP
    • MCM
    • organizers
      Fabrizio Andreatta, Giovanni Catino, Fabio E. G. Cipriani, Gregorio Falqui, Vincenzo Marra, Kevin Payne, Giuseppe Savaré, Thomas Weigel
    • The departments of mathematics of the major Milano universities (Università di Milano, Politecnico di Milano, Università di Milano-Bicocca and Università Bocconi) are pleased to announce the inaugural cycle of a new distinguished lecture series, entitled: The Mathematics Colloquium of Milano Breakthroughs and Perspectives Over the years to come, mathematicians of international prominence will present and discuss the most important new ideas and breakthroughs in contemporary mathematics and its applications. Each lecture should be suitable for a general mathematical audience, especially Ph.D. students and Post-docs. The inaugural cycle of lectures is scheduled to take place from early April until mid-July of 2025.
    • Thursday, 3 April 2025 - Thursday, 10 July 2025
      Milano
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
Upcoming events

  • apr 07 mon 2025

    apr 09 wed 2025

    		WorkShop
    1st workshop on data science for health and biology - ds4hb
    04/07/2025 - 04/09/2025
    logo matematica
    • WORKSHOP
    • DS4HB
    • organizers
      Francesca Ieva, Lara Cavinato, Anna Paganoni, Laura Savarè, Vittorio Torri, Giacomo Boracchi, Emanuele Di Angelantonio e Michela Massi
    • DS4HB will bring together the brightest minds in data science, healthcare, and biology for a unique event designed to inspire dialogue, collaboration, and innovation in this multidisciplinary research field. The workshop is organized in 3 thematic days - Data Science for Omics (Day 1), Data Science for Imaging (Day 2) and Data Science for Electronic Health Records (Day 3) - and offers a broad landscape of invited talks, panel discussions, training and networking events. Featuring a diverse blend of perspectives and internationally renowned speakers, DS4HB provides a platform for cutting-edge ideas to flourish and for the next generation of researchers to learn from the leaders shaping the future of the life sciences.
    • Monday, 7 April 2025 - Wednesday, 9 April 2025
      Politecnico di Milano, Milan (IT)
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • apr 08 tue 2025

    		Seminar
    Khazhgali Kozhasov, On minimality of determinantal and related varieties,  04-08-2025, 11:00 precise
    logo matematica
    • Seminar
    • Khazhgali Kozhasov
    • Université Côte d'Azur, Nizza
    • On minimality of determinantal and related varieties
    • Tuesday, 8 April 2025 at 11:00 right
    • Aula seminari III piano
    • Abstract
      A submanifold of a Riemannian manifold is called minimal if its mean curvature vector field vanishes. Such submanifolds minimize the Riemannian volume locally around every point. Finding minimal algebraic hypersurfaces of arbitrary degree in the n-dimensional Euclidean space is a long-standing open problem posed by Hsiang. In 2010 Tkachev gave a partial solution to this problem showing that the hypersurface of n x n singular real matrices is minimal. I will discuss the following generalization of this fact to all determinantal matrix varieties: for any m, n and r less than m and n, the (open) variety of m x n real matrices of rank r is minimal. More generally, real tensors of fixed multi-linear rank form a minimal submanifold in the space of all tensors of a given format. The talk is partially based on a joint work with A. Heaton and L. Venturello.

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

  • apr 10 thu 2025

    		MOX Colloquia
    Mihaela van der Schaar, Can we discover fundamental laws from data using AI?,  04-10-2025, 14:30
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    MOX

    • MOX Colloquia
    • Mihaela van der Schaar
    • University of Cambridge
    • Can we discover fundamental laws from data using AI?
    • Thursday, 10 April 2025 at 14:30
    • Aula IV - Edificio 11 - Architettura
    • Abstract
      Discovering fundamental laws governing systems from observational data has long been a hallmark of scientific inquiry. In this talk, I will discuss how recent advances in AI and machine learning enable the automated discovery of scientific laws and governing equations directly from data, revolutionizing the way we unravel system dynamics in numerous domains, including medicine and pharmacology. I will highlight how AI-driven methods uncover underlying principles, from classical physics to biological systems to medicine, and offer insights into future possibilities—transforming data-driven observations into interpretable and actionable scientific knowledge. Yet, can we push this boundary further—going beyond equations entirely? I will introduce direct semantic modeling, a novel paradigm where AI learns the behavior of dynamical systems directly from data without relying on closed-form equations. This semantic approach offers intuitive, human-interpretable insights into system evolution, marking a transformative leap in scientific discovery. (This talk is based on recent research with Krzysztof Kacprzyk, Tennison Liu and Sam Holt.)
    • Mihaela van der Schaar

      Mihaela van der Schaar

      Mihaela van der Schaar is the John Humphrey Plummer Professor of Machine Learning, Artificial Intelligence and Medicine at the University of Cambridge. In addition to leading the van der Schaar Lab, Mihaela is founder and director of the Cambridge Centre for AI in Medicine (CCAIM). Mihaela was elected IEEE Fellow in 2009 and Fellow of the Royal Society in 2024. She has received numerous awards, including the Johann Anton Merck Award (2024), the Oon Prize on Preventative Medicine from the University of Cambridge (2018), a National Science Foundation CAREER Award (2004), 3 IBM Faculty Awards, the IBM Exploratory Stream Analytics Innovation Award, the Philips Make a Difference Award and several best paper awards, including the IEEE Darlington Award. She was a Turing Fellow at The Alan Turing Institute in London between 2016 and 2024. Mihaela is personally credited as inventor on 35 USA patents, many of which are still frequently cited and adopted in standards. She has made over 45 contributions to international standards for which she received 3 ISO Awards. In 2019, a Nesta report determined that Mihaela was the most-cited female AI researcher in the U.K.

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

  • apr 14 mon 2025

    		MOX Seminar
    Dan Givoli, Mixed-Dimensional Modeling for Time-Dependent Waves,  04-14-2025, 14:00
    logo matematica
    MOX
    MOX Numeth

    • MOX Seminar
    • Dan Givoli
    • Technion – Israel Institute of Technology
    • Mixed-Dimensional Modeling for Time-Dependent Waves
    • Monday, 14 April 2025 at 14:00
    • Aula Saleri
    • Abstract
      In recent years, along with the increase in the size and complexity of computational models, the scenario of mixed-dimensional (e.g., 2D-1D or 3D-2D, and in general HighD-LowD) coupling has drawn a lot of attention. Fields of application where this scenario is of special interest include, among others, (a) blood-flow analysis, (b) hydrological and geophysical flow models, and (c) elastic structures. In this talk we will review and discuss the application of several coupling schemes to time-dependent wave problems governed by the scalar wave equation and by the equations of elastodynamics.
      After providing the motivation for mixed-dimensional modeling, we will consider the hybrid problem at the continuous level. We will discuss the appropriate interface conditions and prove the well-posedness of the hybrid problem. Among the coupling methods for mixed-dimensional models, we will discuss the Panasenko method, the Nitsche method and two versions of the Dirichlet-to-Neumann (DtN) method. The various methods differ in the way they implement the coupling conditions. We will also discuss the appropriate placement of the HighD-LowD interface, and how this can be estimated a priori and a posteriori. The hybrid model is discretized by the finite element method.
      A special challenge is the attack of elastic problems involving out-of-plane bending. The difficulty lies in the fact that there is a mismatch in the type of unknown variables between the HighD and LowD models, and that there is a significant difference between the types of differential equations and between the types of finite elements (C0 vs. C1) used in each part of the problem. We will present an appropriate coupling approach for such problems.
      We will show the results of some numerical experiments using the various methods, and will compare between them in accuracy and efficiency.

      Contatti:
      luca.formaggia@polimi.it

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

  • may 05 mon 2025

    may 07 wed 2025

    		WorkShop
    Meeting on tomography and applications discrete tomography, neuroscience and image reconstruction 19th edition
    05/05/2025 - 05/07/2025
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    • WORKSHOP
    • TAIR
    • organizers
      Dulio Paolo - Politecnico di Milano, Andrea Frosini - Università di Firenze, Silvia Pagani - Università Cattolica del Sacro Cuore di Brescia, Paolo Finotelli - Università di Caen
    • Moving from its original aim of sharing interdisciplinary aspects between the theoretical and the experimental research concerning X-ray tomography image reconstruction, the event has progressively included new topics. These touch on different kinds of inverse problems, ranging from neuroscience to discrete mathematics, to combinatorial structures, to convex geometry involving projections and sections
    • Monday, 5 May 2025 - Wednesday, 7 May 2025
      Dipartimento di Matematica, Politecnico di Milano
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 08 thu 2025

    may 09 fri 2025

    		WorkShop
    Quantum mathematics @ polimi 2025 : quantum information, entanglement and causality
    05/08/2025 - 05/09/2025
    logo matematica
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 19 mon 2025

    may 20 tue 2025

    		WorkShop
    Quantum mathematics @ polimi 2025 : probabilistic methods for open quantum systems
    05/19/2025 - 05/20/2025
    logo matematica
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 26 mon 2025

    may 30 fri 2025

    		WorkShop
    Quantum mathematics @ polimi 2025 : mathematics of condensed matter systems
    05/26/2025 - 05/30/2025
    logo matematica
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 03 tue 2025

    jun 06 fri 2025

    		WorkShop
    Quantum mathematics @ polimi 2025 : recent advances in operator theory and applications
    06/03/2025 - 06/06/2025
    logo matematica
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 12 thu 2025

    jun 13 fri 2025

    		WorkShop
    Financial education – why, what works, what doesn't and for whom
    06/12/2025 - 06/13/2025
    logo matematica
    • WORKSHOP
    • EDUFIN25
    • organizers
      Emilio Barucci
    • The objective of the conference is twofold: the first is to analyse the importance of financial literacy in supporting financial well-being, financial inclusion, financial market development and enabling a wider economic prosperity; the second is to review concrete experiences, comparing what worked and what didn't and for whom. The aim is to have an international conference on best practices in financial education with a multidisciplinary scientific approach involving academia and policy-makers.
    • Thursday, 12 June 2025 - Friday, 13 June 2025
      Politecnico di Milano
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 23 mon 2025

    jun 27 fri 2025

    		WorkShop
    29th international conference on domain decomposition methods
    06/23/2025 - 06/27/2025
    logo matematica
    • WORKSHOP
    • DD29
    • organizers
      Paola F. Antonietti, Lourenco Beirao da Veiga, Silvia Bertoluzza, Michele Botti, Claudio Canuto, Gabriele Ciaramella, Paola Gervasio, Luca Pavarino, Alfio Quarteroni, Simone Scacchi, Christian Vergara
    • The purpose of the meeting is to discuss recent developments in various aspects of domain decomposition methods, bringing together mathematicians, computational scientists, and engineers working on numerical analysis, scientific computing, high-performance computing, machine learning, and computational science with industrial and societal applications. This event is part of the activities of the Department of Exellence 2023-27.
    • Monday, 23 June 2025 - Friday, 27 June 2025
      Politecnico di Milano
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 30 mon 2025

    jul 04 fri 2025

    		WorkShop
    Differential geometry @ l'aquila 2025
    06/30/2025 - 07/04/2025
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    • WORKSHOP
    • organizers
      Lucio Bedulli, Luciano Mari, Giuseppe Pipoli, Mario Santilli, Alberto Roncoroni, Luigi Vezzoni
    • The aim of the workshop is to focus on different recent advances in differential geometry and its applications, with particular emphasis on riemannian, metric and global differential geometry, theory of submanifolds and geometric flows.
    • Monday, 30 June 2025 - Friday, 4 July 2025
      Università degli Studi dell'Aquila
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jul 07 mon 2025

    jul 11 fri 2025

    		WorkShop
    New perspectives in nonlocal and nonlinear pde
    07/07/2025 - 07/11/2025
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    • WORKSHOP
    • organizers
      José Antonio Carrillo (Univ. of Oxford), Antonio Esposito (Univ. dell'Aquila), Filomena Feo (Univ. "Parthenope"), Giuseppe Savarè (Univ. Bocconi), Bruno Volzone (Politecnico di Milano)
    • The goal of this workshop is to gather researchers working in the field of Partial Differential Equations with expertise in nonlocal and nonlinear equations. Among others, one of the simplest mathematical ways to describe many real-world problems is to start from a set of interacting particles, resulting in nonlocal and nonlinear PDEs in the many-particle limit. Despite the past progress in this field, recent discoveries in biology, plasma physics, and data science, among others, shed the lights on new challenges involving nonlocal structures, such as networks or graphs, and highly nonlinear and singular aggregation-diffusion equations. During the workshop we will focus on various mathematical issues in this direction, for instance: micro-macro description of diffusion process, evolutions on graphs, fluxes with nonlinear mobility, fourth-order aggregation-diffusion equations, etc. This workshop is partially funded by the Advanced Grant Nonlocal-CPD: "Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization" of the European Research Council Executive Agency (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 883363).
    • Monday, 7 July 2025 - Friday, 11 July 2025
      Anacapri
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • sep 08 mon 2025

    sep 11 thu 2025

    		WorkShop
    Perspectives in geometric analysis
    09/08/2025 - 09/11/2025
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    • WORKSHOP
    • PGA25
    • organizers
      Giovanni Catino, Dario D. Monticelli, Alberto Roncoroni
    • The aim of the workshop is to focus on different recent advances in geometric analysis and its applications.
    • Monday, 8 September 2025 - Thursday, 11 September 2025
      Aula Consiglio - 7th floor
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • sep 18 thu 2025

    		MOX Colloquia
    Malgorzata Peszynska, Multi-* mathematics and simulations of coupled processes the Arctic,  09-18-2025, 14:00
    logo matematica
    MOX

    • MOX Colloquia
    • Malgorzata Peszynska
    • Department of Mathematics, Oregon State University
    • Multi-* mathematics and simulations of coupled processes the Arctic
    • Thursday, 18 September 2025 at 14:00
    • Sala Consiglio, Edificio 14, Politecnico di Milano
    • Abstract
      We present our joint work with many collaborators on multi-physics and multiple scales, with focus on processes in  the Arctic, a vast and complex environment of great current interest, with physical models sharing some (but not all) features with high alpine environments and other cold regions.  Our interest is in robust, accurate and conservative computational schemes for the multi-physics: thermal, flow and mechanical deformation (TpHM) in the snow, ice and soils responding to the forcings from the environment for which the data is sparse. The models account for multiple phases and components and present challenges due to the presence of free boundary e.g. of freezing/thawing/sublimation, strong dependence of constitutive parameters on the micro-physics of TpHM, disparate time scales, and micro- and macro heterogeneity. We show how to build constitutive relationships for Darcy scale models from the first principles at the interface- and pore-scale by a combination of mathematically rigorous theory, practical computational upscaling, and surrogate data science tools. We illustrate with simulations of practical scenarios.

      Contatto:
      alessio.fumagalli@polimi.it
    • Malgorzata Peszynska

      Malgorzata Peszynska

      Malgorzata Peszynska received her Ph.D. in Mathematics from University of Augsburg, and M.S. and Habilitation from Warsaw University of Technology. She held academic positions at Polish Academy Of Sciences, Warsaw University of Technology, Purdue University, and The University of Texas at Austin. She has been at Oregon State since 2003 as a full professor since 2012. In 2019-21 she served as a Program Director at the NSF DMS (National Science Foundation, Division of Mathematical Sciences). She is a 2024 University Distinguished Professor, 2022-24 Joel Davis Faculty Scholar, AAAS Honorary Fellow; 2021 SIAM Geosciences Career Prize recipient; 2017 Kosciuszko Foundation College of Eminent Scientists, and holder of OSU Mathematics Graduate mentoring award (2016), Joel Davis Excellence award (2016). She is a 2009-10 Fulbright Research Fellow, as well as Mortar Board professor (2004). She believes in "paying it forward" : M. Peszynska also held leadership and service positions at SIAM (Society for Industrial and Applied Mathematics) including President of SIAM Pacific Northwest Section (2018-20) and SIAM Geosciences (2009-10) and AWM (Association for Women in Mathematics), is serving on editorial boards for 4+ journals, and on the Executive Board of Pacific Math Alliance. She directed several postdocs, doctoral, masters and undergraduate students; see MP people. Her research is in broadly defined applied and computational mathematics modeling of real life phenomena, with foundations in analysis and other core mathematics, and with interdisciplinary applications and collaborations in geosciences (hydrology and oceanography), engineering, and material science.

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

  • oct 09 thu 2025

    		MOX Colloquia
    Mark Girolami, Statistical Finite Element Methods,  10-09-2025, 14:00
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    MOX
    MOX Numeth

    • MOX Colloquia
    • Mark Girolami
    • University of Cambridge
    • Statistical Finite Element Methods
    • Thursday, 9 October 2025 at 14:00
    • Aula Consiglio - VII piano
    • Abstract
      The finite element method (FEM) is one of the great triumphs of applied mathematics, numerical analysis and software development. Recent developments in sensor and signalling technologies enable the phenomenological study of complex natural and physical systems. The connection between sensor data and FEM has been restricted to solving inverse problems placing unwarranted faith in the fidelity of the mathematical description of the system under study. If one concedes mis-specification between generative reality and the FEM then a framework to systematically characterise this uncertainty is required. This talk will present a statistical construction of the FEM which systematically blends mathematical description with data observations by endowing the Hilbert space of FEM solutions with the additional structure of a Probability Measure.
    • Mark Girolami

      Mark Girolami

      Mark Girolami is the Sir Kirby Laing Professor of Civil Engineering within the Department of Engineering at the University of Cambridge where he also holds the Royal Academy of Engineering Research Chair in Data Centric Engineering. Prior to joining the University of Cambridge Professor Girolami held the Chair of Statistics in the Department of Mathematics at Imperial College London. He is the Chief Scientist of the Alan Turing Institute, which is the UK national institute for Data Science and AI. Professor Girolami is an elected fellow of the Royal Academy of Engineering and the Royal Society of Edinburgh, he was an EPSRC Advanced Research Fellow (2007-2012), an EPSRC Established Career Research Fellow (2012-2018), a recipient of a Royal Society Wolfson Research Merit Award, and in 2023 was awarded the Guy Medal in Silver by the Royal Statistical Society. He delivered the IMS Medallion Lecture at the Joint Statistical Meeting 2017, and the Bernoulli Society Forum Lecture at the European Meeting of Statisticians 2017.

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