• 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.

Today's events
Upcoming events
  • 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
    logo matematica
    • 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 19 wed 2024

    Seminar
    Athanasios Kouroupis, Brennan's conjecture for semigroups of holomorphic functions,  06-19-2024, 17:00 precise
    logo matematica
    • Seminar
    • Athanasios Kouroupis
    • Norwegian University of Science and Technology, Trondheim
    • Brennan's conjecture for semigroups of holomorphic functions
    • Wednesday, 19 June 2024 at 17:00 right
    • On-line (il link verrà reso disponibile il giorno stesso del seminario)
    • Abstract
      J. E. Brennan in 1978 conjectured that the p-integral means of the derivative of a univalent function in the unit disk are finite whenever p is between -2 and 2/3. Brennan's conjecture is one of the most famous remaining open problems in the field of geometric function theory. It is known that the conjecture holds for the values between -1.752 and 2/3. This talk aims to give a short and elementary proof of the conjecture in the special case where the univalent function can be embedded into a non-elliptic continuous semigroup of holomorphic functions in the unit disk. This is joint work with Alexandru Aleman.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 20 thu 2024

    Seminar
    Daniela Bertacchi, A new stochastic order applied to branching random walks,  06-20-2024, 11:00
    logo matematica
    • Seminar
    • Daniela Bertacchi
    • Università di Milano-Bicocca
    • A new stochastic order applied to branching random walks
    • Thursday, 20 June 2024 at 11:00
    • Aula Seminari Mox VI piano - Zoom: polimi-it.zoom.us/j/98506199710?pwd=XQWObX8sheg0QTOpRhovbDS7ozxYl0.1
    • Abstract
      Stochastic ordering is a powerful tool to compare random variables and processes.
      We introduce a new type of stochastic ordering which generalizes the germ order introduced by Hutchcroft in 2022, which uses the generating function of the process.
      We apply this order to compare different branching random walks on a countable space $X$. We prove that given two branching random walks with law $\mu$ and $\nu$ respectively, with $\mu\ge\nu$, then in every set where there is extinction according to $\mu$, there is extinction also according to $\nu$. Moreover, in every set where there is strong local survival according to $\nu$, there is strong local survival also according to $\mu$, provided that the supremum of the global extinction probabilities, for the
      $\nu$-process, taken over all starting points $x$, is strictly smaller than 1. New conditions for survival and strong survival for inhomogeneous branching random walks are provided.
      We also extend a result of Moyal (1962), on the properties of fixed points of the generating function of a branching random walk.
    • Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

  • jun 21 fri 2024

    Seminar
    Enrico Valdinoci, Nonlocal minimal surfaces: regularity, stickiness, sheeting phenomena,  06-21-2024, 11:00 precise
    logo matematica
    • Seminar
    • Enrico Valdinoci
    • University of Western Australia
    • Nonlocal minimal surfaces: regularity, stickiness, sheeting phenomena
    • Friday, 21 June 2024 at 11:00 right
    • Sala Consiglio, settimo piano, Dipartimento di Matematica, Edificio 14 "La Nave", Politecnico di Milano
    • Abstract
      At a large scale, minimal solutions of long-range phase coexistence equations tend to separate pure phases through an interface minimizing a nonlocal perimeter functional. These new geometric objects have something in common with classical minimal surfaces, but also exhibit several new and very specific patterns, which we will try to investigate and present.
    • 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
    logo matematica
    • 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 01 mon 2024

    Seminar
    Nicolas Zadeh, Description and numerical study of a kinetic Fokker-Planck equation in neuroscience,  07-01-2024, 15:15
    logo matematica
    • Seminar
    • Nicolas Zadeh
    • Université Libre de Bruxelles, Belgium
    • Description and numerical study of a kinetic Fokker-Planck equation in neuroscience
    • Monday, 1 July 2024 at 15:15
    • Aula seminari MOX, VI piano
    • Abstract
      The well-known Integrate and fire model in a partial differential equation form has been at the center of many mathematical developments since Brunel's work and the seminal paper by Caceres, Carrillo and Perthame in 2011. Its descriptive shortcomings such as the inability to see sub-threshold oscillations or to obtain resonances gave birth to the resonate and fire model (Izhikevich, 2001), phenomenologically complex enough but computationally not costly.
      However, there has been no deep mathematical study of it yet. In this work, we first establish a PDE corresponding to the mean-field limit of a population of resonate and fire neurons.
      The obtained formulation corresponds to a non-linear kinetic Fokker-Planck equation, with a non-local linearity and a measure source term, studied on a half plane. Even though the obtained operator has properties of hypoellipticity, the theoretical study is tedious, encouraging the pursuit of a numerical study to obtain information about the behaviour of the solutions.
      We thereby will describe the positivity and mass preserving finite differences scheme of experimental order one we developed, which allows us to observe all the properties we were expecting from the original single neuron model, and even giving birth to some conjectures which we shall detail.
    • 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
      Scientific and Organizing Committee 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)
    • The second edition of the HPCSIM Workshop—Frontiers of High-Performance Computing in Modeling and Simulation—will take place at Politecnico di Milano, Milan, Italy, from July 4 to 5, 2024. It aims to gather experts on the most recent and effective methodologies for accelerating simulation software on massively parallel platforms. With the contributions of three keynote speakers and fifteen invited speakers, the workshop will provide researchers and practitioners with a survey of HPC's potentiality in a wide range of real-world applications. Registration is free of charge but mandatory at the workshop web site https://www.mate.polimi.it/events/HPCSIM24/ The initiative is co-organized by the MOX Laboratory with M3E SrL and supported by ICSC - National Center in High-Performance Computing, Big Data, and Quantum Computing, European Union – NextGenerationEU and the MUR project, Department of Excellence 2023-27 of the Department of Mathematics of Politecnico di Milano. We gratefully acknowledge the sponsorship by Eni SpA (www.eni.com), E4 Computer Engineering ( https://www.e4company.com/), NVIDIA (https://www.nvidia.com/en-us/) (platinum sponsors), and CFD FEA SERVICE (https://cfdfeaservice.it/) (gold sponsor).
    • 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
    logo matematica
    • 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
    logo matematica
    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 07 thu 2024

    nov 08 fri 2024

    WorkShop
    Mathematics for our health (m4h) workshop
    11/07/2024 - 11/08/2024
    logo matematica
    • WORKSHOP
    • M4H24
    • organizers
      Pasquale Ciarletta, Luca Dedè, Francesca Ieva, Riccardo Sacco, Laura Sangalli, Paolo Zunino
    • M4H workshop brings together leading experts at the intersection of mathematics, data science, and medical research to investigate innovative models for improving medical care. Presentations will focus on showcasing how mathematical and computational techniques can support the development of precision medicine, optimize the allocation of health resources, and enhance the analysis and management of multimodal patients' data. Participants will learn about innovative approaches to improve patient care, from early diagnosis to personalized treatment strategies.
    • Thursday, 7 November 2024 - Friday, 8 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 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

  • 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