PhD Courses

Courses 2025-26
SSD	Name of the course	Professor	Semester	Language	Credits
MAT/05 (BA)	Elliptic-parabolic degenerate operators	Biagi, Bramanti	Spring	English	5
SECS-S/01 (BA)	Advanced Statistical Learning for complex data	Ieva		English	5
MAT/07 (BA) MAT/06	Introduction to Entropy	Jaksic	Winter	English	5
MAT/08 (BA) MAT/03	Analytic and topological aspects in Scientific Machine Learning	Lella, Regazzoni	Winter	English	5
MAT/08 (SC)	Numerical Algorithms for Optimization	Formaggia, Verani	Winter	English	5
MAT/05 (SC)	Some mathematical aspects of Nonlinear Diffusion	Muratori, Volzone	Winter	English	5
	Advanced mathematical methods in engineering I	Correggi			5
	Advanced mathematical methods in engineering II	Correggi			5

Upcoming events

mar 16 mon 2026

MOX Seminar
Alfio Borzì, Reservoir Computing for Scientific Modeling and Data Analysis, 03-16-2026, 10:30
- MOX Seminar
- Alfio Borzì
- University of Wuerzburg
- Reservoir Computing for Scientific Modeling and Data Analysis
- Monday, 16 March 2026 at 10:30
- Aula Saleri
- Abstract
  
  A survey of reservoir computing (RC) as a dynamical framework for learning, classification, prediction, and data analysis is presented. Three reservoir architectures are considered: the echo-state network, a FitzHugh-Nagumo excitable network, and a transformer-inspired reservoir, which are implemented to perform tasks of increasing complexity: learning logical functions, physics-informed solving of the damped harmonic oscillator (including autonomous rollout), image classification with an untrained convolutional front-end, and multi-input RC for CLIP-style language-image pre-training.
  
  Contatto:
  gabriele.ciaramella@polimi.it
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
mar 19 thu 2026

MOX Seminar
Nicola Rares Franco, From operator learning to reduced order modeling and artificial intelligence: a mathematical journey, 03-19-2026, 11:00
- MOX Seminar
- Nicola Rares Franco
- Politecnico di Milano, DMAT, MOX Lab
- From operator learning to reduced order modeling and artificial intelligence: a mathematical journey
- Thursday, 19 March 2026 at 11:00
- Aula Saleri
- Abstract
  
  The idea of learning from physical simulations has now emerged as a promising avenue for addressing the computational challenges posed by many-query applications, such as optimal control, uncertainty quantification and more. Within the literature, we can identify at least three fundamental constituents: (i) operator learning, which leverages approximation theory and functional analysis to come up with rigorous constructions; (ii) reduced order modeling, which combines tools from numerical analysis and PDE theory; and (iii) artificial intelligence, with a stronger data-centric and statistical core.
  
  In this talk, I will focus on the interplay between these three research areas, presenting a series of mathematical results that aim to reconcile domain heuristics with rigorous theoretical guarantees, in an attempt to provide a clearer picture of an otherwise highly complex panorama. To this end, I will first discuss the importance of (nonlinear) low-rank structures, presenting some numerical experiments and related theoretical results featuring deep autoencoders and adaptive basis methods. These will include considerations on the choice of the latent dimension, design of the architectures and a recent note on parametric regularity. As a second step, I will shift the focus to other relevant aspects such as model expressivity, sample complexity, and physical consistency. There, I will present some theoretical contributions and outline specialized strategies for the design of physically-compliant deep learning models. Lastly, I will provide a brief overview about ongoing activities, mostly focusing on the development of probabilistic surrogates via generative AI.
  
  Contatto:
  andrea1.manzoni@polimi.it
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
mar 19 thu 2026

MOX Seminar
Sofia Botti, Multiscale Computational Modeling of Heterogeneous Stem-Derived Cardiac Tissues, 03-19-2026, 11:45
- MOX Seminar
- Sofia Botti
- Politecnico di Milano, DMAT, MOX Lab
- Multiscale Computational Modeling of Heterogeneous Stem-Derived Cardiac Tissues
- Thursday, 19 March 2026 at 11:45
- Aula Saleri
- Abstract
  
  The interpretation of electrophysiological measurements in in vitro cardiac models raises fundamental mathematical and computational questions. In particular, multielectrode array (MEA) recordings provide only indirect access to the underlying cellular dynamics, and their quantitative meaning depends critically on the continuum models and numerical discretizations used to describe the tissue-electrode system.
  
  In this seminar, I present a multiscale computational framework based on the bidomain theory for 2D heterogeneous derived cardiac tissues, extended to account for electrode-tissue coupling. We compare three modeling paradigms: the classical bidomain model, a formulation with electrode- specific boundary conditions, and a fully coupled MEA model including electrode feedback. Although grounded in the same biophysical principles, these approaches lead to distinct variational formulations and algebraic structures, with relevant implications for stability, accuracy, and computational scalability.
  Building on this setting, I discuss a large-scale in-silico correlation study between field potential (FP) biomarkers and action potential (AP) features in tissues composed of atrial-like and ventricular-like phenotypes. By combining bidomain simulations with a 256-electrode MEA representation, we quantify how spatial sampling and tissue heterogeneity affect FP-AP correlations, identifying the FP metrics that most reliably reflect AP properties.
  
  Overall, the proposed framework provides a predictive and mechanistic bridge between cellular electrophysiology and experimentally accessible MEA readouts, supporting a more rigorous interpretation of cardiac assays based on stem derived cardiomyocytes.
  
  Contatto:
  andrea1.manzoni@polimi.it
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
mar 19 thu 2026

MOX Colloquia
Sebastian Geiger, Modelling for understanding – old problems and new challenges for the energy transition, 03-19-2026, 14:00
- MOX Colloquia
- Sebastian Geiger
- Delft University of Technology
- Modelling for understanding – old problems and new challenges for the energy transition
- Thursday, 19 March 2026 at 14:00
- Sala Consiglio, Dipartimento di Matematica, Politecnico di Milano
- Abstract
  
  Geoenergy applications beyond hydrocarbons will play an essential role in accelerating the energy transition: Carbon capture and storage (CCS) is one of the most important approaches to mitigate CO2 emissions; approximately 50% of the energy consumed in the northern hemisphere is needed for heating and cooling, and the expanded use of geothermal energy could lead to significant CO2 reduction; the development of a hydrogen economy for power, transport, and production will rely on intermittent hydrogen storage in geological formations or salt caverns.
  
  All these low-carbon geoenergy applications need bespoke reservoir modelling approaches to estimate available pore volumes for storage, capture how fluids with vastly different properties (e.g. hydrogen vs. hot water) interact with multi-scale geological heterogeneities, and quantify possible operational risks (e.g., early breakthrough of cold water during geothermal energy extraction) while accounting for the uncertainties inherent to geological formations.
  
  This talk will explore how mathematical techniques could be adapted to overcome limitations in existing modelling approaches for low-carbon geoenergy applications. Such new modelling approaches should help to ensure that we design meaningful reservoir models that can provide reservoir performance forecasts with reliable uncertainty bounds, which are needed for new geoenergy applications to advance our transition to a low-carbon energy future.
  
  Contatto:
  alessio.fumagalli@polimi.it
- Sebastian Geiger
  Prof. Dr. Sebastian Geiger, FREng, FRSE, FGS is the Professor of Sustainable Geoenergy and Energi Simulation Chair at the Department of Geoscience and Engineering at the Delft University of Technology. Before joining the Delft University of Technology in 2022, he spent 16 years at Heriot-Watt University where he held the Energi Simulation Chair for Fractured and Geothermal Reservoirs, was the Director of the Institute of Geoenergy Engineering, and was Director of Research for the School of Energy, Geoscience, Infrastructure, and Society.
  
  Sebastian received a PhD degree in Computational Geology from ETH Zurich in 2004 and worked at ETH Zurich as a postdoctoral researcher. He holds an MSc degree in Hydrogeology from Oregon State University (2000) and a Vordiplom (equivalent to BSc degree) in Geology and Mineralogy from the University of Freiburg, Germany (1997). He joined Heriot-Watt University in 2006 as an Assistant Professor and was promoted to Associate Professor in 2009 and Full Professor in 2010.
  
  In 2017 Sebastian received the Alfred Wegener Award from the European Association of Geoscientists and Engineers (EAGE). In 2020 he was appointed as a Fellow of the Royal Society of Edinburgh, Scotland’s national academy of science and letters. In 2022 he was elected as a Fellow of the Royal Academy of Engineering in the UK and in 2024 as a Fellow of the Geological Society of London. He has published over 200 reviewed conference papers and peer-reviewed journals and edited one book. He graduated over 30 PhD students, supervised over 100 MSc project theses, and trained over 10 postdoctoral researchers.
  
  Sebastian is the Editor-in-Chief for the journal Geoenergy and works closely with professional societies such as the European Association of Geoscientists and Engineers. He is also an instructor for HOT Engineering, is a Board Member for the Scottish Energy Forum, and a scientific advisor to NAGRA (Swiss National Cooperative for the Disposal of Radioactive Waste). Together with Dr Hadi Hajibeygi, he created the Geoscience and Geoenergy YouTube Channel, which broadcasts webinars to an audience of over 3700 subscribers across the world.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
mar 19 thu 2026

Seminar
Giulio Schimperna, Some recent results on the so-called ''Cahn-Hilliard-Keller-Segel'' system, 03-19-2026, 14:30
- Seminar
- Giulio Schimperna
- Università di Pavia
- Some recent results on the so-called ''Cahn-Hilliard-Keller-Segel'' system
- Thursday, 19 March 2026 at 14:30
- Aula Seminari, terzo piano
- Abstract
  
  In this talk we will present some mathematical results regarding the so-called "Cahn-Hilliard-Keller-Segel'' system. This is a recently proposed model which couples the Cahn-Hilliard system for phase separation with a further equation describing the evolution of an additional variable $\sigma$. The main application of the model refers to tumor growth processes, in which the phase variable $\varphi$ represents the local proportion of active cancer cells, whereas $\sigma$ denotes the concentration of a chemical substance (for instance a nutrient or a drug) affecting the evolution of the tumor. In this setting, the equation for $\sigma$ may be characterized by a quadratic cross-diffusion term similar to that occurring in the Keller-Segel model for chemotaxis.
  In the talk we will discuss about existence, uniqueness and regularity of several classes of solutions ("weak", "strong" and "entropic") under various assumptions on the mass and nutrient source terms occurring in the system; in a specific situation we will also analyze the long-time behavior of solutions under the perspective of infinite-dimensional dynamical systems.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
mar 19 thu 2026

Seminar
Horia Cornean, Non-interacting orbital magnetism and bulk-edge correspondence for both Schrödinger and Dirac operators, 03-19-2026, 16:15 precise
- Seminar
- Horia Cornean
- Aalborg Universitet
- Non-interacting orbital magnetism and bulk-edge correspondence for both Schrödinger and Dirac operators
- Thursday, 19 March 2026 at 16:15 right
- Sala Consiglio, VII piano
- Abstract
  
  The main purpose of the talk is to explain what bulk-edge correspondence is for people who, like myself, think that plain operator theory and functional analysis could do as well as K and KK theory. I will present previous and ongoing work with J.-M. Barbaroux, L. Le Treust (Marseille \& Toulon), M. Moscolari (Milano), S. Teufel (Tübingen), E. Stockmeyer (Santiago de Chile), K.S. Sørensen (Aalborg), and N. Raymond (Angers). They cover the Schrödinger case doi.org/10.1007/s00023-024-01501-7, the pure Dirac-Landau case link.springer.com/article/10.1007/s11005-024-01839-3 and the general "infinite mass" Dirac case arxiv.org/abs/2509.17151.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
mar 26 thu 2026

Seminar
Mattia Fogagnolo, Inverse mean curvature flow and scalar curvature in low regularity, 03-26-2026, 11:30 precise
- Seminar
- Mattia Fogagnolo
- Università di Padova
- Inverse mean curvature flow and scalar curvature in low regularity
- Thursday, 26 March 2026 at 11:30 right
- Aula Seminari III piano
- Abstract
  
  I’ll present recent results and works in progress involving the inverse mean curvature flow in 3-manifolds endowed with metrics
  of nonnegative scalar curvature. I’ll discuss applications to quasilocal and global mass lower bounds, that will be shown to be stable under uniform limits of the metric tensor. Finally, I will touch upon refined results in progress on the well posedness of the inverse mean curvature flow in such limit spaces, together with applications.
  The talk is based on joint works and projects with Antonelli, Benatti, Gatti, Mazzieri, Nardulli, Pluda and Pozzetta.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 15 wed 2026

WorkShop
Climate risk seminar
04/15/2026
- WORKSHOP
- CLIMRISK
  Climate risk seminar
- organizers
  Emilio Barucci
- QFinLab promotes a series of thematic seminars on climate risk. Climate transformations have a deep impact on economic activity with implications ranging from the definition of green transition policies to the evaluation of financial assets, from the construction of innovative financial and insurance products to risk management, from the design of mechanisms incentive to asset management and much more. Themes that pose intriguing questions to the academic world, involving, those who deal with models to interpret a phenomenon that by its nature is very complex. The activities are organized through a series of double seminars with discussants. April, 15 2026 Seminar room VI floor 15.00-17.00 Department of Mathematics - Luca Trapin (Università di Bologna) Critical Peak Pricing or Rebate? An Impact Analysis in a Cold Climate Market - Andrea Tarelli (Università Cattolica del Sacro Cuore) Structural Pricing of Physical Climate Risk in CDS Markets This event has been (partially) supported by MUR, Department of Excellence 2023-27
- Wednesday, 15 April 2026 - Wednesday, 15 April 2026
  Department of mathematics, VI floor room
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
apr 16 thu 2026

MOX Colloquia
Carola-Bibiane Schönlieb, Mathematical Imaging in the Era of AI, 04-16-2026, 14:00
- MOX Colloquia
- Carola-Bibiane Schönlieb
- Head of the Cambridge Image Analysis group, University of Cambridge
- Mathematical Imaging in the Era of AI
- Thursday, 16 April 2026 at 14:00
- Sala Consiglio, Edificio 14, Politecnico di Milano
- Abstract
  
  Mathematical imaging has for decades been a powerful catalyst for new developments across the mathematical sciences. At its core lie fundamental questions about how information can be represented, reconstructed, and interpreted from incomplete, noisy, or indirect data. Addressing these questions has led to deep advances in areas such as functional and harmonic analysis, geometry, variational methods, inverse problems, partial differential equations, probability and statistics, and, more recently, learning theory. The resulting interplay between theory, computation, and applications has made imaging a uniquely fertile meeting point for pure and applied mathematics alike. Applications span an extraordinary range of domains, including biomedical and materials imaging, astronomy, environmental science, cultural heritage, and emerging technologies such as autonomous systems and data-driven diagnostics.
  The rapid rise of artificial intelligence is now reshaping the landscape of imaging science once again. Data-driven approaches, in particular deep learning, have achieved remarkable empirical success in tasks such as reconstruction, segmentation, and synthesis. At the same time, their opaque nature and heavy reliance on data raise fundamental mathematical questions concerning stability, generalisation, interpretability, uncertainty quantification, and the incorporation of prior knowledge and physical constraints.
  In this talk, I will present mathematical imaging as a continuing source of new mathematical ideas and challenges in the age of AI. I will highlight how modern approaches seek to blend data-driven models with structure, geometry, and physical principles, giving rise to novel analytical frameworks and computational paradigms. This perspective positions imaging not merely as an application area, but as a driver for the next generation of mathematical theory at the interface of analysis, computation, and learning.
  
  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:
  laura.sangalli@polimi.it
  paola.antonietti@polimi.it
- Carola-Bibiane Schönlieb
  Carola-Bibiane Schönlieb is Professor of Applied Mathematics at the University of Cambridge. There, she is head of the Cambridge Image Analysis group. Since 2011 she is a fellow of Jesus College Cambridge. Her current research interests focus on variational methods, partial differential equations and machine learning for image analysis, image processing and inverse imaging problems, and the mathematical foundations of machine learning. She has active interdisciplinary collaborations with clinicians, biologists and physicists on biomedical imaging topics, chemical engineers and plant scientists on image sensing, as well as collaborations with artists and art conservators on digital art restoration.
  Her research has been acknowledged by scientific prizes, among them the LMS Whitehead Prize 2016, the Philip Leverhulme Prize in 2017, the Calderon Prize 2019, a Royal Society Wolfson fellowship in 2020, a doctorate honoris causa from the University of Klagenfurt in 2022, and by invitations to give invited lectures at several renowned applied mathematics conferences, including SIAM, ICM and ICIAM. She is also a SIAM fellow, and ELLIS fellow and a fellow of the Academy of the Mathematical Sciences.
  Carola graduated from the Institute for Mathematics, University of Salzburg (Austria) in 2004. From 2004 to 2005 she held a teaching position in Salzburg. She received her PhD degree from the University of Cambridge (UK) in 2009. After one year of postdoctoral activity at the University of Göttingen (Germany), she became a Lecturer at Cambridge in 2010, promoted to Reader in 2015, promoted to Professor in 2018, and elected to the Professorship of Applied Mathematics (2006) in 2025. Carola convened the European Women in Mathematics Association between 2016 and 2020 and chaired the Committee for Applications and Interdisciplinary Relations (CAIR) of the EMS from 2021 to 2025. She also has been holding several leadership positions at SIAM.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 04 mon 2026

may 06 wed 2026

WorkShop
Meeting on tomography and applications discrete tomography, neuroscience and image reconstruction 20th edition
05/04/2026 - 05/06/2026
- WORKSHOP
- TAIR
  Meeting on tomography and applications discrete tomography, neuroscience and image reconstruction 20th edition
- organizers
  Paolo Dulio - Politecnico di Milano; Paolo Finotelli – Université de Caen Normandie; Andrea Frosini - Università degli Studi di Firenze; Silvia Pagani - Università Cattolica del Sacro Cuore
- This is the 20th edition of the Meeting, whose original aim was to share interdisciplinary aspects between the experimental research concerning X-ray tomography and the mathematical image reconstruction community. In the years, the focus of the Meeting moved from strictly tomographic subjects to different topics, where some kinds of inverse problems are considered. So, different contributions coming from several research areas are now included in the program of the Meeting, such as neuroscientific imaging, discrete mathematic approaches to image reconstructions, combinatorial aspects, projections and sections properties of convex sets
- Monday, 4 May 2026 - Wednesday, 6 May 2026
  Dipartimento di Matematica, 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 15 mon 2026

jun 19 fri 2026

WorkShop
Indam workshop: geometry of severi varieties and hurwitz spaces
06/15/2026 - 06/19/2026
- WORKSHOP
- Indam workshop: geometry of severi varieties and hurwitz spaces
- organizers
  K. Christ, S. Molcho, S. Torelli
- Hurwitz spaces and Severi varieties are among the most classical spaces studied in algebraic geometry, going back to the beginnings of modern algebraic geometry in the second half of the 19th century. Since that time, they have remained central objects in the theory of algebraic curves. Though very classical objects, new techniques have in recent years been used to find answers to old questions, and to establish many new connections. The aim of the workshop is to bring together experts in these various approaches in order to explore further applications and possible synergies. Particular areas of focus are the global geometry of Severi varieties and Hurwitz spaces, as well as relations to Brill Noether theory and to the moduli space of curves and its subloci.
- Monday, 15 June 2026 - Friday, 19 June 2026
  Palazzone di Cortona, Cortona, Italy.
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 29 mon 2026

jul 03 fri 2026

WorkShop
Commutative algebra and algebraic geometry in milan
06/29/2026 - 07/03/2026
- WORKSHOP
- CAAG26
  Commutative algebra and algebraic geometry in milan
- organizers
  A. Constantinescu, A. D'Alì, P. Lella, A. Sammartano
- The conference will be focused on the interplay between topics in commutative algebra, such as syzygies and singularities, and topics in algebraic geometry, such as moduli spaces and rationality problems. Speakers Ayah Almousa (University of Kentucky) Benjamin Briggs (Imperial College London) David Eisenbud (UC Berkeley) Eleonore Faber (University of Graz) Gavril Farkas (Humboldt-Universität zu Berlin) Michele Graffeo (SISSA Trieste) Eloísa Grifo (University of Nebraska-Lincoln) Srikanth Iyengar (University of Utah) Joachim Jelisiejew (University of Warsaw) Patricia Klein (Texas A&M University) Margherita Lelli-Chiesa (Università degli Studi Roma Tre) Alex Massarenti (Università degli Studi di Ferrara) Irena Peeva (Cornell University) Claudia Polini (University of Notre Dame) Elisa Postinghel (Università degli Studi di Trento) Claudiu Raicu (University of Notre Dame) Ritvik Ramkumar (University of Notre Dame) Francesco Russo (Università degli Studi di Catania) Alexandra Seceleanu (University of Nebraska-Lincoln) Bernd Ulrich (Purdue University) Keller VandeBogert (University of Kentucky) Matteo Varbaro (Università degli Studi di Genova
- Monday, 29 June 2026 - Friday, 3 July 2026
  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
aug 31 mon 2026

sep 03 thu 2026

WorkShop
Late summer conference in geometric analysis
08/31/2026 - 09/03/2026
- WORKSHOP
- Late summer conference in geometric analysis
- organizers
  Luca Benatti, Mattia Fogagnolo, Alessandra Pluda, Marco Pozzetta, Alberto Roncoroni.
- This event brings together an international group of specialists to discuss cutting-edge topics in Geometric Analysis, such as minimal surfaces, isoperimetric problems, Lorentzian geometry, general relativity, geometric evolution equations, and geometric problems in the calculus of variations. Our goal is to turn recent progress into meaningful exchanges, giving participants fresh insights and new techniques to use in their own research on open problems.
- Monday, 31 August 2026 - Thursday, 3 September 2026
  Università degli Studi di Padova
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 01 thu 2026

MOX Colloquia
Rainer Helmig, Porous Media Free-Flow Coupling - From REV to Pore Scale and Back, 10-01-2026, 14:30
- MOX Colloquia
- Rainer Helmig
- Professor Emeritus, University of Stuttgart
- Porous Media Free-Flow Coupling - From REV to Pore Scale and Back
- Thursday, 1 October 2026 at 14:30
- Sala Consiglio, Edificio 14, Politecnico di Milano
- Abstract
  
  Flow and transport processes in domains composed of a porous medium and an adjacent free-flow region appear in a wide range of industrial, bio-medical and environmental applications. Industrial applications range from flow in fuel cells to drying processes; possible bio-medical applications include the interplay of distribution processes in blood vessels and in the surrounding tissue. Applications in environmental systems include infiltration of overland flow during rainfall, groundwater contamination due to infiltrating pollutants and evaporation from soil.
  
  One of the key challenges for coupled free flow and porous-medium flow arises from the fact that the overall effective behaviour depends strongly on interface processes that occur on small spatial scales (pore scale), although the overall system of interest is often too large to resolve these processes explicitly in detail. REV-scale models are usually not able to capture all the relevant physical processes for such coupled systems. For the accurate description of interface phenomena, it is therefore necessary to develop model concepts that combine information gained through pore-scale and REV-scale models.
  
  The first part of the lecture includes the following items:
  -an explanation of relevant processes of mass, momentum and energy transfer at the interface between a free-flow and a porous-media system;
  -a presentation of conceptual models for coupled single-phase free flow and two-phase porous-medium flow with a detailed description of the models in the free flow and in the porous medium for the pore and REV scale;
  -comparison studies to show the advantages and disadvantages in relation to classical approaches; the coupling concepts are discussed on the basis of different technical or environmental issues.
  
  In the second part of the lecture I would very much like to discuss the results on the basis of various detailed use cases. These include e.g. aspects of soil evaporation, heat storage in porous media, self-cooling of turbines or the salinization of soils.
  
  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
- Rainer Helmig
  Rainer Helmig is Professor Emeritus of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart, Germany. He gained his doctoral degree from the University of Hannover in 1993 and a the Habilitation degree from the University of Stuttgart in 1997. In 1995, he was awarded the renowned "Dresdner Grundwasserforschungspreis" for his doctoral thesis. From 1997 to 2000, he held a professorship at the Technical University of Braunschweig. He was co-founder and, from 2009 to 2011, President of "InterPore"; from 2007 to 2015, he was spokesman of the International Research Training Group "NUPUS - Nonlinearities and upscaling in porous media", and from 2018 to 2023 he was spokesman of the Collaborative Research Centre 1313 “Interface-Driven Multi-Field Processes in Porous Media: Flow, Transport and Deformation”. From 2007 to 2018, he was a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is member of Academy of Sciences, Academia Europaea, Heidelberg and acatech. In 2020, he was granted the AGU Fellowship of the American Geophysical Union. In 2022 he got the Honorary Degree of Doctor of Engineering at the Heriot-Watt University. He was awarded the Kimberly-Clark Distinguished Lectureship 2025 and in 2025 he was granted the SIAM Geosciences Career Prize.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
nov 02 mon 2026

nov 06 fri 2026

WorkShop
Model reduction and surrogate modeling 2026
11/02/2026 - 11/06/2026
- WORKSHOP
- MORe2026
  Model reduction and surrogate modeling 2026
- organizers
  Andrea Manzoni (Chair), Nicolò Botteghi, Luca Dede', Nicola Farenga, Nicola Rares Franco, Andrea Manzoni, Simona Perotto, Piermario Vitullo, Paolo Zunino (Organizing Committee)
- This 5-day conference will bring together the international community of computational scientists, engineers, mathematicians, and domain experts from industry, the national laboratories and academia to address the topic of model reduction and surrogate modeling for high-dimensional complex systems.
- Monday, 2 November 2026 - Friday, 6 November 2026
  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
jul 05 mon 2027

jul 09 fri 2027

WorkShop
International conference on spectral and high-order methods
07/05/2027 - 07/09/2027
- WORKSHOP
- ICOSAHOM2027
  International conference on spectral and high-order methods
- organizers
  P.F. Antonietti, N. Parolini, M. Verani (Conference Chairs), C. Canuto, A. Quarteroni (Honorary Chairs), L. Beirao da Veiga, F. Bonizzoni, L. Dede’, I. Fumagalli, P. Gervasio, C. Marcati, L. Mascotto, I. Mazzieri, S. Perotto, G. Sangalli
- Since 1989, the International Conference on Spectral and High-Order Methods (ICOSAHOM) has served as a leading international forum for researchers and practitioners working on the theoretical, computational, and applied aspects of high-order and spectral methods for solving differential equations. The 2027 edition of ICOSAHOM will be proudly hosted by Politecnico di Milano, bringing together experts from around the world to share the latest advances and foster new collaborations in this vibrant field. ICOSAHOM 2027 is a satellite meeting of the 11th International Congress on Industrial and Applied Mathematics (ICIAM), The Hague, The Netherlands, 12-16 July 2027.
- Monday, 5 July 2027 - Friday, 9 July 2027
  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

PhD program on

Mathematical Models and Methods in Engineering

PhD Courses