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
  • mar 06 wed 2024

    mar 27 wed 2024

    WorkShop
    Le equazioni differenziali: perché, verso quali direzioni
    03/06/2024 - 03/27/2024
    logo matematica
    • WORKSHOP
    • LED
    • organizers
      Responsabile del corso: Marco Bramanti Docenti del corso: Marco Bramanti, Elsa Marchini, Gianmaria Verzini
    • Le equazioni differenziali (ordinarie) costituiscono un argomento che in base alle indicazioni ministeriali andrebbe trattato nell'ultimo anno di tutti i licei. Per gli insegnanti affrontare questo argomento impegnativo al termine di un percorso già molto denso pone problemi didattici importanti. Cosa scegliere? Di cosa parlare e come?
    • Wednesday, 6 March 2024 - Wednesday, 27 March 2024
      Milano
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • mar 19 tue 2024

    Seminar
    Kenneth DeMason, A Strong Form of the Quantitative Wulff Inequality for Crystalline Norms,  03-19-2024, 15:00
    logo matematica
    • Seminar
    • Kenneth DeMason
    • The University of Texas at Austin
    • A Strong Form of the Quantitative Wulff Inequality for Crystalline Norms
    • Tuesday, 19 March 2024 at 15:00
    • Aula seminari - III piano
    • Abstract
      The anisotropic perimeter is a natural functional appearing in the mathematical framework for determining equilibrium states of crystals in media. As with the usual isotropic perimeter there is an analogous anisotropic isoperimetric inequality, known as the Wulff inequality, where minimizers of the volume constrained anisotropic perimeter problem, known as Wulff shapes, are characterized. In view of statistical mechanics, almost-minimizers are the most likely observable states; as such their identification is just as important as the absolute minimizers. In this talk we will explore a recent result by the speaker which proves quantitative control on almost-minimizers in an H^1 sense when the Wulff shape is a polytope, an upgrade from the previous L^2 control via the so-called Fraenkel asymmetry.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

Upcoming events
  • mar 25 mon 2024

    mar 27 wed 2024

    WorkShop
    Fractals, quantum graphs and applications in pure and applied sciences
    03/25/2024 - 03/27/2024
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    • WORKSHOP
    • organizers
      Fabio E. G. Cipriani (Politecnico di Milano) Simone Creo (Sapienza Università di Roma) Daniele Guido (Università di Roma Tor Vergata) Maria Rosaria Lancia (Sapienza Università di Roma) Diego D. Noja (Università degli Studi di Milano Bicocca)
    • The Workshop is the continuation of the meeting on “Fractals in Pure and Applied Sciences”, held in Rome in March 2023. The aim is to bring together researchers working in the area of fractals, irregular shapes and quantum graphs with a special focus on applications.
    • Monday, 25 March 2024 - Wednesday, 27 March 2024
      Politecnico di Milano, Building 14 “La Nave”, 6th floor - Aula Saleri (Dep. of Mathematics)
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • mar 25 mon 2024

    Seminar
    Annalisa Grossi, Automorphisms of OG10 towards Enriques manifolds,  03-25-2024, 15:30 precise
    logo matematica
    • Seminar
    • Annalisa Grossi
    • Université Paris-Saclay
    • Automorphisms of OG10 towards Enriques manifolds
    • Monday, 25 March 2024 at 15:30 right
    • Aula seminari III piano
    • Abstract
      Automorphisms of hyperkähler manifolds have been studied for many different reasons: construct symplectic quotients or study fixed loci in order to find examples of irreducible symplectic varieties, define maps among different deformation families of HK manifolds, find new examples of Enriques manifolds, that are higher dimensional analogue of Enriques surfaces, and for which Pacienza and Sarti recently proved the Morrison-Kawamata cone conjecture. In the first part of the talk I will show a recent result about symplectic rigidity of hyperkähler manifolds of OG10 type. Then I will show how to construct examples of Enriques manifolds considering nonysmplectic automorphisms of a Laza—Saccà—Voisin manifold that are induced by a nonysmplectic automorphism of the underlying cubic fourfold. The talk is based on a joint work with L. Giovenzana, Onorati and Veniani and on a joint work in progress with Billi, F. and L. Giovenzana.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • apr 11 thu 2024

    MOX Seminar
    Michele Benzi, Revisiting the Augmented Lagrangian Approach to Saddle-Point Problems,  04-11-2024, 14:00
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    MOX
    MOX Numeth

    • MOX Seminar
    • Michele Benzi
    • Scuola Normale Superiore, Pisa
    • Revisiting the Augmented Lagrangian Approach to Saddle-Point Problems
    • Thursday, 11 April 2024 at 14:00
    • Online (trasmesso anche in aula Saleri)
    • Abstract
      Augmented Lagrangian (AL) methods have a long history in both optimization and numerical PDEs, going back to the work of Powell and Hestenes in the late 1960s and to the work of Glowinski and collaborators starting in the mid-1970s, respectively. Whereas AL-type methods have been long very popular in the field of constrained optimization, where are among the most widely used techniques available (as witnessed, for instance, by the great success enjoyed by methods like ADMM), the track record of these methods in solving PDE-related problems has been until recently somewhat less impressive, due in part to ill-conditioning and implementation difficulties.
      In this talk I will describe advances in developing robust and scalable solvers for PDE-related saddle point problems by means of iterative methods and block preconditioners tailored to the AL formulation. The effectiveness of these solvers will be demonstrated on problems from incompressible flow (Oseen problem, coupled Stokes-Darcy problem), liquid crystal directors modeling, and optimal control with PDE constraints. Collaborators over the years include Fatemeh Beik, Chiara Faccio, Patrick Farrell, Santolo Leveque, Maxim Olshanskii and Zhen Wang.

      Contatto:
      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

  • apr 16 tue 2024

    Seminar
    Barbara Guardabascio, Climate and environmental attention: a news-based composite indicator,  04-16-2024, 16:30 precise
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    • Seminar
    • Barbara Guardabascio
    • Università Perugia
    • Climate and environmental attention: a news-based composite indicator
    • Tuesday, 16 April 2024 at 16:30 right
    • Politecnico di Milano Aula IV (accanto aula Rogers)
    • Abstract
      The way people perceive the risks associated with climate change is influenced by scientific research, social awareness, and by media representation Boykoff [2011]. The effects of perception of climate risk extend beyond Environmental concerns and permeate decision-making processes in both economic and social policy.
      We believe that a composite index to measure climate attention, if well-constructed and robust, can provide valuable insights for policymakers and serve as a leading indicator in macroeconomic and financial analysis [Luxon, 2019]. The composite indicator proposed in this article is based on a novel methodology that evaluates the semantic relevance, and not the favorability, of selected keywords, each of them provided with a semantic score, based both on the number of appearances and on the interconnectedness with other words in the text corpus.
      Finally, the Benefit of the Doubt (BoD) aggregation strategy is adopted that takes advantage of a time-varying optimal weighting scheme. The index is compared to alternative approaches.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • apr 16 tue 2024

    Seminar
    Viola Schiaffonati, L'etica dell'intelligenza artificiale fra vecchi problemi e nuove sfide,  04-16-2024, 17:30
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    • Seminar
    • Viola Schiaffonati
    • Politecnico di Milano
    • L'etica dell'intelligenza artificiale fra vecchi problemi e nuove sfide
    • Tuesday, 16 April 2024 at 17:30
    • Aula Rogers e in collegamento webex su tiny.cc/mathseminars
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • apr 18 thu 2024

    Seminar
    Elena Danesi, Strichartz estimates for the Dirac equation on compact manifolds without boundary,  04-18-2024, 15:00
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    • Seminar
    • Elena Danesi
    • Università di Padova
    • Strichartz estimates for the Dirac equation on compact manifolds without boundary
    • Thursday, 18 April 2024 at 15:00
    • Aula seminari - III piano
    • Abstract
      The Dirac equation on Rn can be listed within the class of dispersive equations, together with, e.g., the wave and Klein-Gordon equations. In the years a lot of tools have been developed in order to quantify the dispersion of a system. Among these one finds the Strichartz estimates, that are a priori estimates of the solutions in mixed Lebesgue spaces. For the flat case Rn they are known, as they are derived from the ones that hold for the wave and Klein-Gordon equations. However, when passing to a curved spacetime domain, very few results are present in the literature. In this talk I will firstly introduce the Dirac equation on curved domains. Then, I will discuss the validity of this kind of estimates in the case of Dirac equations on compact Riemannian manifolds without boundary. This is based on a joint work with Federico Cacciafesta (Università di Padova) and Long Meng (CERMICS-École des ponts ParisTech).
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 06 mon 2024

    may 08 wed 2024

    WorkShop
    Meeting on tomography and applications discrete tomography, neuroscience and image reconstruction 18th edition
    05/06/2024 - 05/08/2024
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    • WORKSHOP
    • TAIR
    • organizers
      Paolo Dulio - Politecnico Milano, Paolo Finotelli – Université de Caen Normandie, Andrea Frosini - Universita' Firenze, Silvia Pagani - Universita' Cattolica,
    • The aim of the Meeting is to share interdisciplinary aspects between the experimental and the mathematical research concerning image reconstruction, with a special focus on tomography and neuroscience
    • Monday, 6 May 2024 - Wednesday, 8 May 2024
      Mathematics Department - 7th floor
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • may 06 mon 2024

    may 10 fri 2024

    WorkShop
    The geometry of hilbert schemes of points
    05/06/2024 - 05/10/2024
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    • WORKSHOP
    • GHiSP
    • organizers
      Michele Graffeo (SISSA), Paolo Lella (Polimi), Sergej Monavari (EPFL), Andrea T. Ricolfi (SISSA), Alessio Sammartano (Polimi)
    • The Hilbert scheme is a classically studied moduli space, which parametrises closed subschemes with prescribed Hilbert polynomial in an ambient projective scheme. These moduli spaces where initially introduced by Grothendieck, but turned out to have a prominent rôle in many modern areas outside the realm of Algebraic Geometry: Mathematical Physics, Combinatorics, Theoretical Physics (just to mention some recent examples). Generalisations of the Hilbert scheme have a wide range of applications as well, such as nested Hilbert schemes (parametrising flags of closed subschemes), moduli spaces of framed sheaves and Quot schemes (parametrising quotient sheaves). The easiest example one can consider is the Hilbert scheme of points, which parametrises closed zero-dimensional subschemes of fixed length. Already in this case, the geometry of the moduli space is rich and intriguing, as it is in general considerably pathological. For instance, if the dimension of the ambient variety is 3, the Hilbert scheme of points is in general reducible, and for dimension larger than 4 its singularities can be as bad as possible. Hilbert schemes (and their generalisation) played an important role in the development of modern Enumerative Geometry. In fact, for a large and interesting class of cases, the Hilbert scheme of points is not smooth but carries a virtual fundamental class. Donaldson-Thomas theory deals precisely with the (virtual) invariants one can compute on the Hilbert schemes with respect to its virtual structure. Donaldson-Thomas theory is very rich and admits several layers of refinements, for example: cohomological, K-theoretical, elliptic, categorical, motivic and is predicted to match Gromov-Witten invariants. SPEAKERS Alessandra Bernardi, Gergely Bérczi, Nadir Fasola, Anthony Iarrobino, Joachim Jelisiejew, Tomasz Mandziuk, Cristina Manolache, Alina Marian, Rosa Maria Miro-Roig, Andrei Negut, Ritvik Ramkumar, Ilaria Rossinelli, Reinier F. Schmiermann, Roy Skjelnes
    • Monday, 6 May 2024 - Friday, 10 May 2024
      BellaVista Relax Hotel, Levico Terme (TN), Italy
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • may 07 tue 2024

    Seminar
    Annalisa Panati, Fisica a teatro: lo strano caso di Wolfgang Pauli,  05-07-2024, 17:30
    logo matematica
    • Seminar
    • Annalisa Panati
    • Università di Tolone
    • Fisica a teatro: lo strano caso di Wolfgang Pauli
    • Tuesday, 7 May 2024 at 17:30
    • Aula Rogers e in collegamento webex su tiny.cc/mathseminars
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 29 wed 2024

    Seminar
    Paolo Cremonesi, La magia dei Computer Quantistici,  05-29-2024, 17:30
    logo matematica
    • Seminar
    • Paolo Cremonesi
    • Politecnico di Milano
    • La magia dei Computer Quantistici
    • Wednesday, 29 May 2024 at 17:30
    • Aula T12 e in collegamento webex su tiny.cc/mathseminars
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 05 wed 2024

    jun 07 fri 2024

    WorkShop
    Perspectives in pdes, global and functional analysis
    06/05/2024 - 06/07/2024
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    • WORKSHOP
    • organizers
      Matteo Bonforte (Universidad Autónoma de Madrid, Spain) Matteo Muratori (Politecnico di Milano, Italy) Fabio Punzo (Politecnico di Milano, Italy) Alberto Setti (Università degli Studi dell'Insubria, Italy)
    • This workshop aims at bringing together world experts from Analysis and Geometry, with a particular accent on the broad field of Partial Differential Equations and their applications. In particular, the main topics addressed lie at the interface between Global Analysis, Functional Analysis, Geometric Analysis and Differential Geometry. The meeting is held on the special occasion given by the 60th birthday of Gabriele Grillo, Professor of Mathematical Analysis at Politecnico di Milano since 2009.
    • Wednesday, 5 June 2024 - Friday, 7 June 2024
      Università degli Studi dell'Insubria - Sede di Sant'Abbondio a Como
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • oct 17 thu 2024

    MOX Colloquia
    Marc G. Genton, Exascale Geostatistics for Environmental Data Science,  10-17-2024, 14:00
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    MOX

    • MOX Colloquia
    • Marc G. Genton
    • King Abdullah University of Science and Technology (KAUST), Saudi Arabia
    • Exascale Geostatistics for Environmental Data Science
    • Thursday, 17 October 2024 at 14:00
    • Aula Consiglio VII piano - Dipartimento di Matematica
    • Abstract
      Environmental data science relies on some fundamental problems such as: 1) Spatial Gaussian likelihood inference; 2) Spatial kriging; 3) Gaussian random field simulations; 4) Multivariate Gaussian probabilities; and 5) Robust inference for spatial data. These problems develop into very challenging tasks when the number of spatial locations grows large. Moreover, they are the cornerstone of more sophisticated procedures involving non-Gaussian distributions, multivariate random fields, or space-time processes. Parallel computing becomes necessary for avoiding computational and memory restrictions associated with large-scale environmental data science applications. In this talk, I will explain how high-performance computing can provide solutions to the aforementioned problems using tile-based linear algebra, tile low-rank approximations, as well as multi- and mixed-precision computational statistics. I will introduce ExaGeoStat, and its R version ExaGeoStatR, a powerful software that can perform exascale (10^18 flops/s) geostatistics by exploiting the power of existing parallel computing hardware systems, such as shared-memory, possibly equipped with GPUs, and distributed-memory systems, i.e., supercomputers. I will then describe how ExaGeoStat can be used to design competitions on spatial statistics for large datasets and to benchmark new methods developed by statisticians and data scientists for large-scale environmental data science.

      Contatti: laura.sangalli@polimi.it
    • Marc G. Genton

      Marc G. Genton

      Marc G. Genton is Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received the Ph.D. degree in Statistics (1996) from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), and is an elected member of the International Statistical Institute (ISI). In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society (TIES) and the Distinguished Achievement award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association (ASA). He received an ISI Service award in 2019 and the Georges Matheron Lectureship award in 2020 from the International Association for Mathematical Geosciences (IAMG). He led a Gordon Bell Prize finalist team with the ExaGeoStat software for Super Computing 2022. He received the Royal Statistical Society (RSS) 2023 Barnett Award for his outstanding research in environmental statistics. His research interests include statistical analysis, flexible modeling, prediction, and uncertainty quantification of spatio-temporal data, with applications in environmental and climate science, as well as renewable energies.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • nov 21 thu 2024

    MOX Colloquia
    Klaus-Robert Müller, Machine Learning and AI for the Sciences: toward understanding,  11-21-2024, 14:00
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    MOX

    • MOX Colloquia
    • Klaus-Robert Müller
    • Technische Universität Berlin
    • Machine Learning and AI for the Sciences: toward understanding
    • Thursday, 21 November 2024 at 14:00
    • Aula Consiglio VII piano
    • Abstract
      In recent years, machine learning (ML) and artificial intelligence (AI) methods have begun to play a more and more enabling role in the sciences and in industry. In particular, the advent of large and/or complex data corpora has given rise to new technological challenges and possibilities. In his talk, Müller will touch upon the topic of ML applications in the sciences, in particular in chemistry and physics. He will also discuss possibilities for extracting information from machine learning models to further our understanding by explaining nonlinear ML models. Finally, Müller will briefly discuss perspectives and limitations.
    • Klaus-Robert Müller

      Klaus-Robert Müller

      Klaus-Robert Müller has been a professor of computer science at Technische Universität Berlin since 2006; at the same time he is directing rsp. co-directing the Berlin Machine Learning Center and the Berlin Big Data Center and most recently BIFOLD . He studied physics in Karlsruhe from 1984 to 1989 and obtained his Ph.D. degree in computer science at Technische Universität Karlsruhe in 1992. After completing a postdoctoral position at GMD FIRST in Berlin, he was a research fellow at the University of Tokyo from 1994 to 1995. In 1995, he founded the Intelligent Data Analysis group at GMD-FIRST (later Fraunhofer FIRST) and directed it until 2008. From 1999 to 2006, he was a professor at the University of Potsdam. From 2012 he has been Distinguished Professor at Korea University in Seoul. In 2020/2021 he spent his sabbatical at Google Brain as a Principal Scientist. Among others, he was awarded the Olympus Prize for Pattern Recognition (1999), the SEL Alcatel Communication Award (2006), the Science Prize of Berlin by the Governing Mayor of Berlin (2014), the Vodafone Innovations Award (2017), Hector Science Award (2024), Pattern Recognition Best Paper award (2020), Digital Signal Processing Best Paper award (2022). In 2012, he was elected member of the German National Academy of Sciences-Leopoldina, in 2017 of the Berlin Brandenburg Academy of Sciences, in 2021 of the German National Academy of Science and Engineering and also in 2017 external scientific member of the Max Planck Society. From 2019 on he became an ISI Highly Cited researcher in the cross-disciplinary area. His research interests are intelligent data analysis and Machine Learning in the sciences (Neuroscience (specifically Brain-Computer Interfaces, Physics, Chemistry) and in industry.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568