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
  • may 27 mon 2024

    may 31 fri 2024

    WorkShop
    Wave dynamics and fluid-structure interactions
    05/27/2024 - 05/31/2024
    logo matematica
    • WORKSHOP
    • WDFS
    • organizers
      Maurizio Garrione e Filippo Gazzola (Politecnico di Milano), Riccardo Montalto (Università degli Studi di Milano)
    • The school will be based on scientific topics such as the Navier-Stokes and Euler equations, turbulence, fluid-structure interactions, water waves, normal forms and KAM for PDEs, dispersive PDEs. Putting together experts in these fields should give a somehow global overview on the main current research lines on fluids. This school is supposed to attract the interest of young and experienced researchers and stimulate collaborations and discussions.
    • Monday, 27 May 2024 - Friday, 31 May 2024
      Villa del Grumello, Como
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • may 27 mon 2024

    may 28 tue 2024

    WorkShop
    Numbers and stories - ethical dimensions of climate change research
    05/27/2024 - 05/28/2024
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    • WORKSHOP
    • organizers
      Hernan Bobadilla (DMAT), Rawad El Skaf (DMAT), Sara Giarola (DIG/RFF-CMCC), Francesco Nappo (DMAT), Massimo Tavoni (DIG/RFF-CMCC), Henrik Thoren (Lund University), Giovanni Valente (DMAT)
    • The conference will bring together internationally renowned experts and early career researchers for an interdisciplinary discussion on the ethical dimensions of climate change research. Specifically, the first day will be concerned with the theme of illegitimate value influences and the responsibility of scientists and institutions in ensuring relevance and integrity of climate change research. The second day will discuss whether and how considerations of justice should enter the evaluation of mitigation scenarios and how doing so could enhance the credibility and effectiveness of future research. Specific proposals will be discussed for operationalizing justice into quantitative emission scenarios produced by the scientific community.
    • Monday, 27 May 2024 - Tuesday, 28 May 2024
      Politecnico di Milano, Aula Rogers
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
Upcoming events
  • 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

  • may 30 thu 2024

    Seminar
    Andrea Posilicano, Self-adjoint extensions by a Krein-type resolvent formula,  05-30-2024, 10:00
    logo matematica
    • Seminar
    • Andrea Posilicano
    • Università dell'Insubria
    • Self-adjoint extensions by a Krein-type resolvent formula
    • Thursday, 30 May 2024 at 10:00
    • Sala Consiglio, VII piano
    • Abstract
      We present a simple recipe to build all the self-adjoint extensions of a symmetric operator S which is the restriction of a given self-adjoint one. This provides the resolvent of the extensions and requires knowledge of neither the defect spaces nor the adjoint of S. Some applications to quantum mechanical models are given.

      This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • may 31 fri 2024

    Seminar
    Andrea Posilicano, Self-adjoint extensions by a Krein-type resolvent formula,  05-31-2024, 10:00
    logo matematica
    • Seminar
    • Andrea Posilicano
    • Università dell'Insubria
    • Self-adjoint extensions by a Krein-type resolvent formula
    • Friday, 31 May 2024 at 10:00
    • Sala Consiglio, VII piano
    • Abstract
      We present a simple recipe to build all the self-adjoint extensions of a symmetric operator S which is the restriction of a given self-adjoint one. This provides the resolvent of the extensions and requires knowledge of neither the defect spaces nor the adjoint of S. Some applications to quantum mechanical models are given.

      This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
    • 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
  • jun 05 wed 2024

    Seminar
    Martin Kolodziejczyk, McKean-Vlasov SPDEs,  06-05-2024, 15:00
    logo matematica
    • Seminar
    • Martin Kolodziejczyk
    • Politecnico di Milano
    • McKean-Vlasov SPDEs
    • Wednesday, 5 June 2024 at 15:00
    • Aula Seminari - III piano. Zoom: polimi-it.zoom.us/j/92358057734?pwd=dTNBNHZMQVFZVjgrQ0FJMXpOc3BEdz09
    • Abstract
      We consider McKean-Vlasov Stochastic Partial Differential Equations with additive noise. We will focus on their well-posedness and long-time behaviour; showing that, under some assumptions on the spatial regularity of the noise, these SPDEs are well-posed and the semigroup resulting from them is strong Feller and irreducible.
      This is based on joint work with L. Angeli, J. Barrè and M. Ottobre.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 10 mon 2024

    MOX Seminar
    Tan Bui-Thanh, Learn2Solve: A Deep Learning Framework for Real-Time Solutions of forward, inverse, and UQ Problems,  06-10-2024, 14:00
    logo matematica
    MOX
    MOX Numeth

    • MOX Seminar
    • Tan Bui-Thanh
    • The University of Texas at Austin, USA
    • Learn2Solve: A Deep Learning Framework for Real-Time Solutions of forward, inverse, and UQ Problems
    • Monday, 10 June 2024 at 14:00
    • Aula Saleri
    • Abstract
      Digital models (DMs) are designed to be replicas of systems and processes. At the core of a digital model (DM) is a physical/mathematical model that captures the behavior of the real system across temporal and spatial scales. One of the key roles of DMs is enabling “what if” scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, to calibrate parameters to match the actual process and to quantify the uncertainties. In this talk, we will present various (faster than) real-time Scientific Deep Learning (SciDL) approaches for forward, inverse, and UQ problems. Both theoretical and numerical results for various problems including transport, heat, Burgers, (transonic and supersonic) Euler, and Navier-Stokes equations will be presented.

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

  • jun 14 fri 2024

    WorkShop
    Lombardy young numerical analysts vi
    06/14/2024
    logo matematica
    • WORKSHOP
    • LYNUM VI
    • organizers
      Mattia Corti, Erika Temellini
    • The aim of the meeting is to bring together young researchers in Numerical Analysis and Scientific Computing from universities in Lombardy to exchange their work and foster new connections and potential future collaborations.
    • Friday, 14 June 2024 - Friday, 14 June 2024
      Politecnico di Milano, Aula Rogers
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • jun 17 mon 2024

    Seminar
    Jaqueline Godoy Mesquita, Averaging principles and stability in the context of functional differential equations,  06-17-2024, 15:15
    logo matematica
    • Seminar
    • Jaqueline Godoy Mesquita
    • University of Brasilia
    • Averaging principles and stability in the context of functional differential equations
    • Monday, 17 June 2024 at 15:15
    • Sala Consiglio, settimo piano, Dipartimento di Matematica, Politecnico di Milano
    • Abstract
      In this lecture, we will discuss periodic and nonperiodic averaging principles for functional differential equations, as well as stability results.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 19 wed 2024

    jun 21 fri 2024

    WorkShop
    Kickoff workshop of the erc synergy grant ''nemesis: new generation methods for numerical simulations''
    06/19/2024 - 06/21/2024
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    • WORKSHOP
    • NEMESIS Kickoff Workshop
    • organizers
      Paola F. Antonietti (Politecnico di Milano), Lourenco Beirao da Veiga (Università degli Studi di Milano-Bicocca), Daniele A. Di Pietro (Université de Montpellier), Jerome Droniou (CNRS)
    • The ERC NEMESIS project has been funded in the 2023 Synergy call for a duration of six years. Its goal is to lay the groundwork for a novel generation of numerical simulators by tackling key difficulties of PDE problems of the 21st century: -Incomplete differential operators in Hilbert complexes; -The efficient solution of the discrete problems relating to the latter; -The presence of nonlinear and hybrid-dimensional multi-physics, encountered in applications such as geological flows or magneto-hydrodynamics. The NEMESIS project aims at overcoming the above difficulties, therefore boosting the prediction capabilities of numerical simulators in engineering and applied sciences. A key point will be the use of polytopal meshes and the higher-level point of view provided by polytopal constructions. This kick-off workshop will gather a community of mathematicians and engineers working in the broad field of the project, to foster exchanges and promote long-term collaborations.
    • Wednesday, 19 June 2024 - Friday, 21 June 2024
      Montpellier (FR)
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • jun 26 wed 2024

    jun 28 fri 2024

    WorkShop
    Nonlinear pdes: theory and modelling of real phenomena - on the occasion of filippo gazzola's 60th birthday
    06/26/2024 - 06/28/2024
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    • WORKSHOP
    • organizers
      Comitato Scientifico: Elvise Berchio, Alberto Ferrero, Maurizio Garrione - Comitato Organizzatore: Edoardo Bocchi, Alessio Falocchi, Clara Patriarca, Gianmarco Sperone
    • Provide a dynamic platform for researchers, scholars, and practitioners to converge and exchange insights on the latest developments in the field of nonlinear partial differential equations (PDEs). This interdisciplinary gathering seeks to foster collaborative discussions on the theoretical foundations and practical applications of nonlinear PDEs, exploring their pivotal role in accurately modeling and understanding complex real-world phenomena.
    • Wednesday, 26 June 2024 - Friday, 28 June 2024
      Riemann International School of Mathematics (RISM), Varese
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • jul 02 tue 2024

    MOX Seminar
    Patrick Vega, An adaptive superconvergent mixed finite element method based on local residual minimization,  07-02-2024, 14:00
    logo matematica
    MOX
    MOX Numeth

    • MOX Seminar
    • Patrick Vega
    • Universidad de Santiago de Chile
    • An adaptive superconvergent mixed finite element method based on local residual minimization
    • Tuesday, 2 July 2024 at 14:00
    • Aula Saleri
    • Abstract
      We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal variable with an adaptive finite element method via residual minimization. Such a residual minimization procedure is performed on a local postprocessing scheme, commonly used in the context of mixed finite element methods. Given the local nature of that approach, the underlying saddle point problems associated with residual minimizations can be solved with minimal computational effort. We propose and study a posteriori error estimators, including the built-in residual representative associated with residual minimization schemes; and an improved estimator that adds, on the one hand, a residual term quantifying the mismatch between discrete fluxes and, on the other hand, the interelement jumps of the postprocessed solution. We present numerical experiments in two dimensions using Brezzi-Douglas-Marini elements as input for our methodology. The experiments perfectly fit our key theoretical findings and suggest that our estimates are sharp.

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

  • jul 04 thu 2024

    jul 05 fri 2024

    WorkShop
    Hpcsim - frontiers of high-performance computing in modeling and simulation
    07/04/2024 - 07/05/2024
    logo matematica
    • WORKSHOP
    • HPCSIM2024
    • organizers
      Luca Formaggia, Paolo Cremonesi, Carlo de Falco, Ivan Fumagalli, Ilario Mazzieri, Nicola Parolini (Politecnico di Milano), Carlo Janna, Andrea Franceschini (Università di Padova), Nicolò Spiezia (M3E)
    • HPCSIM aims to explore recent methodologies to accelerate simulation software on massively parallel platforms and provide researchers and practitioners with a survey on the potential of HPC in real-world applications. Registration at https://www.mate.polimi.it/events/HPCSIM24/"
    • Thursday, 4 July 2024 - Friday, 5 July 2024
      Politecnico di Milano, Leonardo Campus - Aula Rogers
    Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
  • sep 09 mon 2024

    sep 11 wed 2024

    WorkShop
    13th symposium on conformal and probabilistic prediction with applications
    09/09/2024 - 09/11/2024
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    • WORKSHOP
    • COPA 2024
    • organizers
      Simone Vantini (General Chair); Matteo Fontana (Programme Chair); Alfredo Gimenez Zapiola, Teresa Bortolotti, Khuong An Nguyen (Organizing Chairs); Francesca Ieva (Stakeholder Relation Chair)
    • Conformal prediction (CP) is a modern machine and statistical learning method that allows to develop valid predictions under weak probabilistic assumptions. CP can be used to form set predictions, using any underlying point predictor, and for very general target variables, allowing the error levels to be controlled by the user. Therefore, CP has been widely used to develop robust forms of probabilistic prediction methodologies, and applied to many practical real life challenges. The aim of this symposium is to serve as a forum for the presentation of new and ongoing work and the exchange of ideas between researchers on any aspect of conformal and probabilistic prediction, including their application to interesting problems in any field.
    • Monday, 9 September 2024 - Wednesday, 11 September 2024
      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
  • sep 19 thu 2024

    MOX Colloquia
    Jay Gopalakrishnan, From scalar to tensor finite elements,  09-19-2024, 14:00
    logo matematica
    MOX

    • MOX Colloquia
    • Jay Gopalakrishnan
    • Portland State University
    • From scalar to tensor finite elements
    • Thursday, 19 September 2024 at 14:00
    • Aula Consiglio VII piano - Dipartimento di Matematica
    • Abstract
      In the history of finite elements, the earliest Lagrange finite elements, consisted of scalar-valued functions. To approximate fluxes, vector-valued finite elements with continuous normal (n) components across element interfaces, or n-continuous elements, were developed later. The finite element toolkit was then supplemented by t-continuous vector-valued Nedelec elements with continuous tangential (t) components, now routinely used for Maxwell equations. Although these elements were developed separately, today we understand them together as fitting into a cochain subcomplex of a de Rham complex of Sobolev spaces.
      Other tensor-valued finite elements are now being viewed with increasing interest and they form the main subject of this talk. The earliest of these consists of matrix-valued functions whose normal-normal (nn) component varies continuously across element interfaces: these are the nn-continuous matrix fields of the Hellan-Herrmann-Johnson element. More recently, nt-continuous matrix-valued finite elements were developed to approximate viscous stress in incompressible flows: they have continuous shear, or normal-tangential (nt) components. To add to this picture, matrix-valued elements with continuous tangential-tangential (tt) components, called Regge elements, are finding increasing utility: they are key to approximating the metric tensor of Riemannian manifolds. This talk delves into the details of these developments.
      How does one connect these disparate developments with nn-, nt-, and tt-continuous matrix finite elements? This does not appear to be as easy as the previous synthesis of vector-valued elements by the de Rham complex. The spaces in de Rham complexes are connected by fundamental first-order differential operators (grad, curl, and div in three dimensions), all derived from a single definition of the exterior derivative. In contrast, what is natural for the above-mentioned tensor finite elements are other second-order differential operators. We conclude grazing the frontiers of our understanding on potentially unifying connections.

      This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

      Contatti:
      paola.antonietti@polimi.it
      gabriele.ciaramella@polimi.it
      ilario.mazzieri@polimi.it
    • Jay Gopalakrishnan

      Jay Gopalakrishnan

      Jay Gopalakrishnan is a computational mathematician whose research centers around improving accuracy and efficiency of finite element methods for partial differential equations. He co-invented two classes of numerical methods, now known as the discontinuous Petrov Galerkin (DPG) methods, and the hybridizable discontinuous Galerkin (HDG) methods. He has co-authored over ninety publications, has served in the editorial boards of seven journals, including service as one of the managing editors. He earned his PhD in 1999 under the supervision of James Bramble and Joseph Pasciak He then worked at Bell Labs, Medtronic Inc, University of Minnesota, and was a mathematics professor at University of Florida for over a decade. He currently holds an endowed chair at Portland State University in Oregon, where he is engaged in a variety of regional activities to bolster scientific computation.
    • 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 11 mon 2024

    nov 12 tue 2024

    WorkShop
    Mathematics for planet earth
    11/11/2024 - 11/12/2024
    logo matematica
    • WORKSHOP
    • M4E24
    • organizers
      Daniele Marazzina, Edie Miglio, Simona Perotto, Anna Scotti, Simone Vantini, Marco Verani, Michele Botti, Alessio Fumagalli, Andrea Gilardi, Ilario Mazzieri, Alessandra Menafoglio
    • This workshop is designed to unveil the critical role of mathematics in understanding and addressing the challenges that confront our planet. Leading experts will present different topics: from climate change analysis to resource management and conservation efforts. Participants will be introduced to cutting-edge mathematical approaches that offer insights into preserving our world.
    • Monday, 11 November 2024 - Tuesday, 12 November 2024
      Politecnico di Milano, Milan, Italy
    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
    logo matematica
    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

  • dec 05 thu 2024

    MOX Colloquia
    Ilaria Perugia, Structure-preserving discretization of cross-diffusion systems,  12-05-2024, 14:00
    logo matematica
    MOX

    • MOX Colloquia
    • Ilaria Perugia
    • University of Vienna
    • Structure-preserving discretization of cross-diffusion systems
    • Thursday, 5 December 2024 at 14:00
    • Aula Consiglio VII piano - Dipartimento di Matematica
    • Abstract
      Several applications in physics, biology, and chemistry involve systems with multiple components, such as gas mixtures, competing population species, and reacting chemical substances. These problems are modeled with nonlinear reaction-diffusion equations that include cross-diffusion terms. Cross diffusion occurs when the flux of one component is driven by the gradient of another component. The main challenges in designing numerical methods for approximating nonlinear cross-diffusion systems are that the diffusion matrix may not be symmetric or positive semidefinite, and that a maximum principle may not be available. In this talk, we present numerical methods based on the boundedness-by-entropy framework introduced by A. Jüngel in 2015. Motivated by the inherent entropy structure of the PDE system, nonlinear transformations involving the entropy variable allow for the enforcement of positivity in the approximate solutions. Specifically, we focus on a Local Discontinuous Galerkin method. By appropriately introducing auxiliary variables, the problem is reformulated so that nonlinearities do not appear within differential operators or interface terms. This results in nonlinear operators that can be naturally evaluated in parallel. The method allows for arbitrary degrees of approximation in space, preserves boundedness of the physical unknowns without requiring postprocessing or slope limiters, and satisfies a discrete version of the entropy stability estimate of the continuous problem.

      Contatto: paola.antonietti@polimi.it
    • Ilaria Perugia

      Ilaria Perugia

      Ilaria Perugia is professor of Numerics of Partial Differential Equations at the University of Vienna, Austria. She received her PhD in 1999 from the University of Milano, Italy, under the supervision of Franco Brezzi. She held posts at the University of Pavia (university researcher, associate professor, full professor), as well as visiting positions at the University of Minnesota and at ETH Zürich. She was appointed professor at the University of Vienna in 2013. Since 2016, she has been deputy director of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in Vienna. She is serving in the editorial boards of several journals in Numerical Analysis and Scientific Computing. Her research is concerned with finite element methods for the numerical approximation of partial differential equations. Her interests mainly focus on the design and the analysis of standard and non standard finite element methods (discontinuous Galerkin, virtual element methods, finite elements with operator-adapted basis functions, space-time methods).
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568