PhD program on Mathematical Models and Methods in Engineering - Dipartimento di Matematica

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)

Numerical simulation of blood flow in the heart
(courtesy of Prof. Alfio Quarteroni)

Objectives

The development of advanced technologies in Science and Engineering brings an increasing demand of advanced mathematical theories and methods, which in turn fosters the demand for education and training of skilled mathematicians in pure and applied research. The main scope of the Ph.D. course “Mathematical Models and Methods in Engineering” is to train high-level researchers in various fields of pure and applied mathematics.

Professional Opportunities

Expected professional placements for Ph.D. doctorates are: academic research in Italian or International Universities and Research Institutions, R & D divisions of private companies, study and research centers of public Agencies, financial and insurance Institutions.

Upcoming events

sep 19 thu 2024

MOX Colloquia
Jay Gopalakrishnan, From scalar to tensor finite elements, 09-19-2024, 14:00
- 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 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
- 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 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
- WORKSHOP
- M4H24
  Mathematics for our health (m4h) workshop
- 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 07 thu 2024

nov 08 fri 2024

WorkShop
Algodefi24 workshop
11/07/2024 - 11/08/2024
- WORKSHOP
- ALGODEFI24
  Algodefi24 workshop
- organizers
  Emilio Barucci (Politecnico di Milano) Andrea Prampolini (Intesa Sanpaolo) Michele Azzone (Politecnico di Milano)
- Algo-trading & DeFi Methods and Technologies The landscape of financial markets is changing significantly thanks to new technologies and methodologies that are modifying their architecture and functioning. Among the innovations, we have the possibility of using real-time market information, machine learning techniques, automatic trading strategies, automatic market making, distributed ledger technologies, digital assets, smart contracts, cryptocurrencies with deep consequences concerning asset pricing, computational finance, market microstructure, customer protection, financial education. The objective of the workshop is to offer an opportunity for the academic and industrial communities to meet together and discuss research advancements on these topics.
- Thursday, 7 November 2024 - Friday, 8 November 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
nov 11 mon 2024

nov 12 tue 2024

WorkShop
Mathematics for planet earth
11/11/2024 - 11/12/2024
- WORKSHOP
- M4E24
  Mathematics for planet earth
- 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
- 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 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
- 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 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
jan 27 mon 2025

jan 29 wed 2025

WorkShop
Regularity and geometric aspects of nonlinear pdes, milan 2025
01/27/2025 - 01/29/2025
- WORKSHOP
- Regularity and geometric aspects of nonlinear pdes, milan 2025
- organizers
  Stefano Biagi and Benedetta Noris
- The present workshop is organized with the support of the project MUR-PRIN project 2022R537CS “NO3 – Nodal optimization, nonlinear elliptic equations, nonlocal geometric problems, with a focus on regularity”, granted by the European Union – Next Generation EU. The aim is to bring together both young researchers and recognized experts on regularity and geometric aspects of nonlinear PDEs, in order to present and discuss recent results obtained within the aforementioned project.
- Monday, 27 January 2025 - Wednesday, 29 January 2025
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 23 mon 2025

jun 27 fri 2025

WorkShop
29th international conference on domain decomposition methods
06/23/2025 - 06/27/2025
- WORKSHOP
- DD29
  29th international conference on domain decomposition methods
- 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