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.

Today's events

apr 03 thu 2025

jul 10 thu 2025

WorkShop
Mathematics colloquium of milano: inaugural cycle
04/03/2025 - 07/10/2025
- WORKSHOP
- MCM
  Mathematics colloquium of milano: inaugural cycle
- organizers
  Fabrizio Andreatta, Giovanni Catino, Fabio E. G. Cipriani, Gregorio Falqui, Vincenzo Marra, Kevin Payne, Giuseppe Savaré, Thomas Weigel
- The departments of mathematics of the major Milano universities (Università di Milano, Politecnico di Milano, Università di Milano-Bicocca and Università Bocconi) are pleased to announce the inaugural cycle of a new distinguished lecture series, entitled: The Mathematics Colloquium of Milano Breakthroughs and Perspectives Over the years to come, mathematicians of international prominence will present and discuss the most important new ideas and breakthroughs in contemporary mathematics and its applications. Each lecture should be suitable for a general mathematical audience, especially Ph.D. students and Post-docs. The inaugural cycle of lectures is scheduled to take place from early April until mid-July of 2025.
- Thursday, 3 April 2025 - Thursday, 10 July 2025
  Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 30 mon 2025

jul 04 fri 2025

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

Upcoming events

jul 07 mon 2025

jul 11 fri 2025

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

MOX Seminar
Jeff Boisvert, The Future of Machine Learning and Model Validation in the Earth Sciences: The Good, the Bad, and the Ugly, 07-11-2025, 10:00
- MOX Seminar
- Jeff Boisvert
- University of Alberta-School of Mining and Petroleum Engineering Civil and Environmental Engineering
- The Future of Machine Learning and Model Validation in the Earth Sciences: The Good, the Bad, and the Ugly
- Friday, 11 July 2025 at 10:00
- Politecnico di Milano, Edificio 14, Aula B.5.3
- Abstract
  
  The earth sciences are being transformed by advances in machine learning (ML) and artificial intelligence. From optimizing mineral estimation and hydrocarbon production to improving wildfire prediction and management, these methods offer exciting opportunities for modeling and decision-making. However, these advances bring challenges with model validation, which is critical for ensuring that predictions are robust, reasonable, and actionable.
  This lecture will delve into the evolving role of ML in the mining, hydrocarbon, or wildfire industry, highlighting successes, pitfalls, and future prospects. "The Good" will explore case studies and implementations where ML has significantly improved modeling, decision making, and inference. "The Bad" will examine common pitfalls, including data biases, overfitting, and the misuse of algorithms without understanding domain constraints. Finally, "The Ugly" will confront the ethical and operational risks posed by poorly validated models, emphasizing the importance of transparency and domain experts.
  This lecture will not only focus on ML methods, but will also consider how to validate all types of earth science models including estimates, simulations, and decision making. We will discuss best practices for integrating ML models into traditional workflows while addressing the complexities of model validation.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

jul 15 tue 2025

jul 16 wed 2025

WorkShop
Workshop 2025 - digimath il ruolo delle tecnologie digitali a supporto della didattica della matematica: esperienze di buone pratiche a livello universitario
07/15/2025 - 07/16/2025

WORKSHOP
DIGiMATH
Workshop 2025 - digimath il ruolo delle tecnologie digitali a supporto della didattica della matematica: esperienze di buone pratiche a livello universitario
organizers
COMITATO SCIENTIFICO Domenico Brunetto Monica Conti Michele G. Fiorentino Annamaria Miranda COMITATO ORGANIZZATORE Caterina Bassi Domenico Brunetto Monica Conti Helena Dell'Anna
Il gruppo UMI DIGiMATH lavora per favorire lo sviluppo della cultura digitale per l'innovazione dei processi di insegnamento e apprendimento della matematica a livello universitario. Lo scopo del workshop è quello di confrontare e discutere le esperienze già in atto nelle università italiane di pratiche e ricerche sull’uso delle tecnologie digitali nella didattica della matematica e promuovere lo sviluppo di collaborazioni tra ricercatori in didattica della matematica e in altre aree della matematica per la definizione di pratiche e ricerche congiunte. I temi di discussione includono quelli già individuati da DIGiMATH e quelli emersi dal precedente Workshop - difficoltà, progettazione, valutazione, individualizzazione/personalizzazione - declinati lungo i tre contesti di transizione scuola/università, corsi di base di matematica, formazione insegnanti (iniziale e in continuo). Lo stile della giornata sarà improntato a favorire la discussione e la collaborazione tra i partecipanti, pertanto sarà dato ampio spazio al confronto e all’elaborazione delle idee. Inoltre, a chiusura del workshop ci sarà una sessione di brainstorming di programmazione di future attività di DIGiMATH.
Tuesday, 15 July 2025 - Wednesday, 16 July 2025
Aula Laboratorio FDS

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

sep 08 mon 2025

sep 11 thu 2025

WorkShop
Perspectives in geometric analysis
09/08/2025 - 09/11/2025
- WORKSHOP
- PGA25
  Perspectives in geometric analysis
- organizers
  Giovanni Catino, Dario D. Monticelli, Alberto Roncoroni
- The aim of the workshop is to focus on different recent advances in geometric analysis and its applications.
- Monday, 8 September 2025 - Thursday, 11 September 2025
  Aula Consiglio - 7th floor
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
sep 18 thu 2025

MOX Colloquia
Malgorzata Peszynska, Multi-* mathematics and simulations of coupled processes the Arctic, 09-18-2025, 14:00
- MOX Colloquia
- Malgorzata Peszynska
- Department of Mathematics, Oregon State University
- Multi-* mathematics and simulations of coupled processes the Arctic
- Thursday, 18 September 2025 at 14:00
- Sala Consiglio, Edificio 14, Politecnico di Milano
- Abstract
  
  We present our joint work with many collaborators on multi-physics and multiple scales, with focus on processes in the Arctic, a vast and complex environment of great current interest, with physical models sharing some (but not all) features with high alpine environments and other cold regions. Our interest is in robust, accurate and conservative computational schemes for the multi-physics: thermal, flow and mechanical deformation (TpHM) in the snow, ice and soils responding to the forcings from the environment for which the data is sparse. The models account for multiple phases and components and present challenges due to the presence of free boundary e.g. of freezing/thawing/sublimation, strong dependence of constitutive parameters on the micro-physics of TpHM, disparate time scales, and micro- and macro heterogeneity. We show how to build constitutive relationships for Darcy scale models from the first principles at the interface- and pore-scale by a combination of mathematically rigorous theory, practical computational upscaling, and surrogate data science tools. We illustrate with simulations of practical scenarios.
  
  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.
  
  Contatto:
  alessio.fumagalli@polimi.it
- Malgorzata Peszynska
  Malgorzata Peszynska received her Ph.D. in Mathematics from University of Augsburg, and M.S. and Habilitation from Warsaw University of Technology. She held academic positions at Polish Academy Of Sciences, Warsaw University of Technology, Purdue University, and The University of Texas at Austin. She has been at Oregon State since 2003 as a full professor since 2012. In 2019-21 she served as a Program Director at the NSF DMS (National Science Foundation, Division of Mathematical Sciences). She is a 2024 University Distinguished Professor, 2022-24 Joel Davis Faculty Scholar, AAAS Honorary Fellow; 2021 SIAM Geosciences Career Prize recipient; 2017 Kosciuszko Foundation College of Eminent Scientists, and holder of OSU Mathematics Graduate mentoring award (2016), Joel Davis Excellence award (2016). She is a 2009-10 Fulbright Research Fellow, as well as Mortar Board professor (2004). She believes in "paying it forward" : M. Peszynska also held leadership and service positions at SIAM (Society for Industrial and Applied Mathematics) including President of SIAM Pacific Northwest Section (2018-20) and SIAM Geosciences (2009-10) and AWM (Association for Women in Mathematics), is serving on editorial boards for 4+ journals, and on the Executive Board of Pacific Math Alliance. She directed several postdocs, doctoral, masters and undergraduate students; see MP people. Her research is in broadly defined applied and computational mathematics modeling of real life phenomena, with foundations in analysis and other core mathematics, and with interdisciplinary applications and collaborations in geosciences (hydrology and oceanography), engineering, and material science.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 09 thu 2025

MOX Colloquia
Mark Girolami, Statistical Finite Element Methods, 10-09-2025, 14:00
- MOX Colloquia
- Mark Girolami
- University of Cambridge
- Statistical Finite Element Methods
- Thursday, 9 October 2025 at 14:00
- Aula Consiglio - VII piano
- Abstract
  
  The finite element method (FEM) is one of the great triumphs of applied mathematics, numerical analysis and software development. Recent developments in sensor and signalling technologies enable the phenomenological study of complex natural and physical systems. The connection between sensor data and FEM has been restricted to solving inverse problems placing unwarranted faith in the fidelity of the mathematical description of the system under study. If one concedes mis-specification between generative reality and the FEM then a framework to systematically characterise this uncertainty is required. This talk will present a statistical construction of the FEM which systematically blends mathematical description with data observations by endowing the Hilbert space of FEM solutions with the additional structure of a Probability Measure.
- Mark Girolami
  Mark Girolami is the Sir Kirby Laing Professor of Civil Engineering within the Department of Engineering at the University of Cambridge where he also holds the Royal Academy of Engineering Research Chair in Data Centric Engineering. Prior to joining the University of Cambridge Professor Girolami held the Chair of Statistics in the Department of Mathematics at Imperial College London. He is the Chief Scientist of the Alan Turing Institute, which is the UK national institute for Data Science and AI. Professor Girolami is an elected fellow of the Royal Academy of Engineering and the Royal Society of Edinburgh, he was an EPSRC Advanced Research Fellow (2007-2012), an EPSRC Established Career Research Fellow (2012-2018), a recipient of a Royal Society Wolfson Research Merit Award, and in 2023 was awarded the Guy Medal in Silver by the Royal Statistical Society. He delivered the IMS Medallion Lecture at the Joint Statistical Meeting 2017, and the Bernoulli Society Forum Lecture at the European Meeting of Statisticians 2017.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 16 thu 2025

oct 17 fri 2025

WorkShop
Algodefi25-algorithmic trading, decentralized finance and artificial intelligence in capital markets
10/16/2025 - 10/17/2025
- WORKSHOP
- ALGODEFI25
  Algodefi25-algorithmic trading, decentralized finance and artificial intelligence in capital markets
- organizers
  Scientific committee: Emilio Barucci (chair), Tomaso Aste, Michele Azzone, Leandro Sánchez Betancourt, Andrea Prampolini
- Call for papers: papers or extended abstract Deadline for submission: September 1st Notification of acceptance: September 15th Deadline for registration: October 1st Keynote speakers: - Paul Besson (Head of Quant Research, Euronext) TBD - Thierry Foucault (HEC Paris) AI-Powered traders and liquidity in securities markets - Martin Herdegen (University of Stuttgart) Optimal Dynamic Fees in Automated Market Makers - Eyal Neumann (Imperial College) Fredholm Approach to Nonlinear Propagator Models The landscape of financial markets is changing significantly thanks to new technologies and methodologies that are profoundly modifying their architecture and functioning. Among the innovations, we have the possibility of operating using real-time market information, machine learning techniques, automatic trading strategies, automatic market making, distributed ledger technologies, digital assets, smart contracts, cryptocurrencies. The objective of the workshop is to offer an opportunity for the academic and industrial communities to meet and discuss research advancements on these topics. Sponsorship: Banca Intesa Sanpaolo, IASON Ltd Under the auspices of ASSIOM FOREX, SHIELD Project
- Thursday, 16 October 2025 - Friday, 17 October 2025
  Politecnico di Milano Venue: Department of Mathematics, Conference Room: Aula Rogers
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 16 thu 2025

MOX Colloquia
Colin Cotter, Compatible finite elements for numerical weather prediction, 10-16-2025, 14:00
- MOX Colloquia
- Colin Cotter
- Imperial College
- Compatible finite elements for numerical weather prediction
- Thursday, 16 October 2025 at 14:00
- Sala Consiglio, Dipartimento di Matematica, Politecnico di Milano
- Abstract
  
  I will discuss the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's “C-grid” finite difference scheme to the finite element world. They are constructed from a discrete de Rham complex, which is a sequence of finite element spaces which are linked by the operators of differential calculus. The use of discrete de Rham complexes to solve partial differential equations is well established, but in this talk I focus on the specifics of dynamical cores for simulating weather, oceans and climate. The most important consequence of the discrete de Rham complex is the Hodge-Helmholtz decomposition, which has been used to exclude the possibility of several types of spurious oscillations from linear equations of geophysical flow. This means that compatible finite element spaces provide a useful framework for building dynamical cores. In this talk I will introduce the main concepts of compatible finite element spaces, and discuss their wave propagation properties. I will then cover a selection of the following topics (depending on recent advances, and interests of the audience): practical application to numerical weather prediction and ocean models, structure preserving methods, and scalable iterative solver techniques.
- Colin Cotter
  Colin Cotter is Professor of Computational Mathematics at Imperial College, researching numerical analysis and scientific computing focusses on the design, analysis and implementation of numerical methods and data assimilation algorithms for weather forecasting, ocean modelling and climate simulation. His work on compatible finite element methods underpins the next generation Met Office forecast modelling system. He has co-authored over 100 journal publications, and co-authored a book with Sebastian Reich on data assimilation published by Cambridge University Press. He has served on the editorial board of three journals. He was awarded a PhD in Mathematics at Imperial in 2004 under the supervision of Sebastian Reich, and subsequently held positions in the departments of Earth Science and Engineering and Aeronautics before rejoining the department of Mathematics in 2014, where he is is currently the head of Applied Mathematics in the Department of Mathematics at Imperia, and is co-Director of the UCL/Imperial EPSRC Centre for Doctoral Training in Collaborative Computational Modelling at the Interface.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568