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

oct 23 fri 2026

Seminar
Valeria Bertini, Rational curves on HK manifolds, 10-23-2026, 11:00 precise
- Seminar
- Valeria Bertini
- Università di Milano
- Rational curves on HK manifolds
- Friday, 23 October 2026 at 11:00 right
- Aula seminari, terzo piano
- Abstract
  
  By a classical theorem of Bogomolov and Mumford, every ample linear system on a projective K3 surface contains a sum of rational curves. As a natural higher-dimensional analogue, we can ask whether every ample class on a projective hyperkähler (HK) manifold has a multiple containing a sum of uniruled divisors. Such divisors are special: by adjunction, smooth ample divisors on varieties with trivial canonical bundle are of general type, hence not uniruled. The question is also motivated by Voisin’s conjectures on the Chow group of 0-cycles, for which ample uniruled divisors provide the first evidence. In this talk I will present the known results on the known deformation families of HK manifolds, including joint work with A. Grossi and work in progress with A. Grossi and G. Nanni.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

Upcoming events

oct 26 mon 2026

WorkShop
A teacup with navier-stokes
10/26/2026
- WORKSHOP
- A teacup with navier-stokes
- organizers
  Alessio Falocchi, Filippo Gazzola
- The objective of this mini workshop is to create a collaborative forum on fluid dynamics, specifically tailored for early-career researchers. The event seeks to facilitate the dissemination of recent advancements in fluid dynamics, stimulate discussion around key unresolved challenges, and encourage the formation of scientific partnerships.
- Monday, 26 October 2026 - Monday, 26 October 2026
  Aula Consiglio - 7th floor, Building 14, Politecnico di Milano, Via Bonardi 9 - 20133 Milano (Italy)
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 27 tue 2026

Seminar
Alessandro Ferreri, Position-space invariants for topological crystalline insulators, 10-27-2026, 11:00 precise
- Seminar
- Alessandro Ferreri
- Università di Roma La Sapienza
- Position-space invariants for topological crystalline insulators
- Tuesday, 27 October 2026 at 11:00 right
- Aula Seminari III piano
- Abstract
  
  The study of topological phases of crystalline insulators leads to the problem of characterizing homotopy classes of Fermi projections associated with gapped Schrödinger operators with space-group symmetries. The Bloch–Floquet decomposition provides a momentum-space description of the occupied states, in which crystalline symmetries give rise to topological invariants that distinguish phases under deformations preserving the spectral gap and the symmetries. The usual formulation of these invariants relies on this momentum-space description and on compatibility of the Fermi projection with the prescribed space-group. This motivates the search for a position-space formulation whose behavior can also be studied when a momentum-space description is unavailable or the symmetries are broken.
  
  In this talk, I will present an operator-theoretic framework for expressing crystalline symmetry invariants directly in position space. The approach combines propagation properties and local trace-class regularity of Fermi projections with Fourier-analytic methods to derive reconstruction formulas relating position-space quantities to the invariants of a crystalline system. I will also discuss the stability of these quantities under perturbations of the Hamiltonian that preserve the spectral gap, highlighting the role of the spatial distribution of the perturbation.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 28 wed 2026

Seminar
Davide Bricalli, On the maximal variation problem, 10-28-2026, 14:00 precise
- Seminar
- Davide Bricalli
- Università di Pavia
- On the maximal variation problem
- Wednesday, 28 October 2026 at 14:00 right
- Aula Seminari III piano
- Abstract
  
  In this talk, we study the maximal variation problem for linear systems associated with a very ample line bundle, using Hodge theory and Picard–Lefschetz theory. We provide an affirmative answer to the maximal variation problem for a broad class of smooth projective varieties. This includes varieties $X$ of dimension $n$ at least 2 with $p_g=h^{n,0}(X)>0$ and $H^{n-1,0}(X)=\{0\}$, Enriques surfaces, irregular surfaces with maximal Albanese dimension, smooth hyperkähler varieties, and all the smooth not Fano hypersurfaces in $\mathbb{P}^n$. As a consequence, by a result of Beauville, we establish a Lefschetz property for the Jacobian rings of smooth hypersurfaces in $\mathbb{P}^n$ of degree at least $n+1$. This is based on a joint work in collaboration with Gian Pietro Pirola.
- 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
nov 04 wed 2026

Seminar
Luca Brandolini, L'analisi di Fourier e la previsione delle maree, 11-04-2026, 15:30
- Seminar
- Luca Brandolini
- Università degli Studi di Bergamo
- L'analisi di Fourier e la previsione delle maree
- Wednesday, 4 November 2026 at 15:30
- Aula Laboratorio FDS - tiny.cc/zoomfds
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
nov 09 mon 2026

nov 13 fri 2026

WorkShop
Two workshops on mathematics for sustainability
11/09/2026 - 11/13/2026
- WORKSHOP
- M4E-M4H
  Two workshops on mathematics for sustainability
- organizers
  M4H - Scientific Committee: Luca Dedè (SC chair), Pasquale Ciarletta, Francesca Ieva, Laura Maria Sangalli, Paolo Zunino; M4H - Organizing Committee: Francesco Regazzoni (OC chair), Francesca Bonizzoni, Ivan Fumagalli, Stefano Pagani, Andrea Signori; M4E - Scientific Committee: Simona Perotto (SC chair), Alessio Fumagalli, Andrea Manzoni, Daniele Marazzina, Edie Miglio, Simone Vantini, Marco Verani; M4E - Organizing Committee: Anna Scotti (OC chair), Michele Azzone, Michele Botti, Gabriele Ciaramella, Carlo De Falco, Ilario Mazzieri, Alessandra Menafoglio
- The second edition of the initiative “Mathematics for Sustainability” will take place in November 2026, as part of the activities of the Department of Excellence, Department of Mathematics, Politecnico di Milano. The initiative is organized into two workshops: Mathematics for Planet Earth (M4E), November 9-11, 2026 Mathematics for our Health (M4H), November 11-13, 2026 Both events will be held at Politecnico di Milano (Leonardo Campus, Aula Rogers). Mathematics for Planet Earth aims to highlight the fundamental role of mathematics in understanding the challenges related to our planet. Presentations will cover several areas, including climate change, resource management, and conservation. Participants will have the opportunity to learn about state-of-the-art mathematical methodologies for understanding and preserving our planet. Mathematics for our Health brings together experts at the intersection of mathematics, data science, and medical research to explore innovative models for improving healthcare. The workshop will focus on how mathematical, computational, statistical, and machine learning techniques can support the development of precision medicine, optimize healthcare resource allocation, and improve the analysis and management of multimodal patient data. Further information is available on the events' webpages: https://www.mate.polimi.it/events/M4H26/ https://www.mate.polimi.it/events/M4E26/
- Monday, 9 November 2026 - Friday, 13 November 2026
  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 18 wed 2026

feb 03 wed 2027

WorkShop
19° ciclo seminari fds
11/18/2026 - 02/03/2027
- WORKSHOP
- Seminari FDS
  19° ciclo seminari fds
- organizers
  Marco Bramanti e Domenico Brunetto
- I seminari FDS, nati nel 2008, sono momenti di riflessione su contenuti e metodi dell’insegnamento scolastico della matematica.
- Wednesday, 18 November 2026 - Wednesday, 3 February 2027
  Aula Laboratorio FDS - http://tiny.cc/zoomfds
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
nov 18 wed 2026

Seminar
Sonia Spreafico, Dalla piega al teorema: l'origami come laboratorio di matematica nella scuola secondaria di secondo grado, 11-18-2026, 15:00
- Seminar
- Sonia Spreafico
- Università degli Studi di Milano
- Dalla piega al teorema: l'origami come laboratorio di matematica nella scuola secondaria di secondo grado
- Wednesday, 18 November 2026 at 15:00
- Aula Laboratorio FDS - tiny.cc/zoomfds
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
nov 25 wed 2026

Seminar
Mattia Ricchi, Fisica medica e imaging biomedico: quando la fisica rende visibile l'invisibile, 11-25-2026, 15:00
- Seminar
- Mattia Ricchi
- Università di Pisa - INFN Bologna
- Fisica medica e imaging biomedico: quando la fisica rende visibile l'invisibile
- Wednesday, 25 November 2026 at 15:00
- Aula Laboratorio FDS - tiny.cc/zoomfds
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
nov 27 fri 2026

WorkShop
Evolution equations & dynamical systems
11/27/2026
- WORKSHOP
- VIS60
  Evolution equations & dynamical systems
- organizers
  Monica Conti, Filippo Dell'Oro, Andrea Giorgini, Maurizio Grasselli
- a tribute to Vittorino Pata for his 60th birthday
- Friday, 27 November 2026 - Friday, 27 November 2026
  Aula Consiglio, Dipartimento di Matematica
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
dec 14 mon 2026

WorkShop
Bridging analysis and geometry
12/14/2026
- WORKSHOP
- Bridging analysis and geometry
- organizers
  Giulia Meglioli, Marco Pozzetta, Alberto Roncoroni
- The workshop brings together early-career researchers in PDEs and Differential Geometry to share recent advancements, discuss open problems, and build new scientific collaborations. This event is supported by INdAM (Istituto Nazionale di Alta Matematica) and by the Department of Mathematics, Politecnico di Milano.
- Monday, 14 December 2026 - Monday, 14 December 2026
  Aula Consiglio - 7th floor, Building 14, Politecnico di Milano, Via Bonardi 9 - 20133 Milano (Italy)
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
dec 16 wed 2026

Seminar
Marco Caroccia, La brachistocrona restaurata, 12-16-2026, 15:00
- Seminar
- Marco Caroccia
- Università degli studi di Firenze
- La brachistocrona restaurata
- Wednesday, 16 December 2026 at 15:00
- Aula Laboratorio FDS - tiny.cc/zoomfds
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jan 13 wed 2027

Seminar
Camilla Spagnolo, Oltre la risposta corretta: riflettere sull'insegnamento della matematica nell'era dell'Intelligenza Artificiale, 01-13-2027, 15:00
- Seminar
- Camilla Spagnolo
- Università degli studi di Ferrara
- Oltre la risposta corretta: riflettere sull'insegnamento della matematica nell'era dell'Intelligenza Artificiale
- Wednesday, 13 January 2027 at 15:00
- Aula Laboratorio FDS - tiny.cc/zoomfds
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jan 27 wed 2027

Seminar
Laura Abatangelo & Sara Maggis, Dal laboratorio di fisica alle funzioni di più variabili: spunti per un'esperienza didattica, 01-27-2027, 15:00
- Seminar
- Laura Abatangelo & Sara Maggis
- Politecnico di Milano, Liceo Statale A. Banfi di Vimercate
- Dal laboratorio di fisica alle funzioni di più variabili: spunti per un'esperienza didattica
- Wednesday, 27 January 2027 at 15:00
- Aula Laboratorio FDS - tiny.cc/zoomfds
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
feb 03 wed 2027

Seminar
Paolo Freguglia, François Viète e la nascita dell'algebra letterale: analisi storica e considerazioni didattiche, 02-03-2027, 15:00
- Seminar
- Paolo Freguglia
- Università de L’Aquila
- François Viète e la nascita dell'algebra letterale: analisi storica e considerazioni didattiche
- Wednesday, 3 February 2027 at 15:00
- Aula Laboratorio FDS - tiny.cc/zoomfds
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
feb 08 mon 2027

feb 12 fri 2027

WorkShop
Mathematical challenges in quantum mechanics 2027, school and workshop
02/08/2027 - 02/12/2027
- WORKSHOP
- MCQM27
  Mathematical challenges in quantum mechanics 2027, school and workshop
- organizers
  Michele Correggi (Polimi), Marco Falconi (Polimi), Davide Fermi (Polimi), Angelo Lucia (Polimi), Massimo Moscolari (Polimi), Alessandro Olgiati (Polimi).
- From February 8th to 12th, 2027, the School and Workshop Mathematical Challenges in Quantum Mechanics (MCQM27) will take place at the Department of Mathematics of Politecnico di Milano (Italy). The meeting – at its fifth edition – aims to present the state of the art of challenging open problems in Quantum Mechanics, from the point of view of Mathematical Physics. It will provide a space for scientific exchanges among PhD students and early-career and senior researchers. The program will consist of three introductory mini courses (by Phan Thành Nam, Yoshiko Ogata, Andreas Winter), six invited talks (by Horia Cornean, Marcello Dalmonte, Clotilde Fermanian Kammerer, Paolo Tilli, Katharina Schratz, Giovanni Valente) and contributed talk sessions by selected young participants. Some financial support to young participants will be available. Website: www.mcqm.it This event is part of the activities of the Department of Exellence 2023-27.
- Monday, 8 February 2027 - Friday, 12 February 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
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
oct 11 mon 2027

oct 15 fri 2027

WorkShop
Advances in computational neurology: mathematical modeling, simulation, and data-driven methods
10/11/2027 - 10/15/2027
- WORKSHOP
- AXON
  Advances in computational neurology: mathematical modeling, simulation, and data-driven methods
- organizers
  Paola F. Antonietti, Francesca Bonizzoni, Ivan Fumagalli, Niteen Kumar, Stefano Pagani
- Computational neurology aims to support neurologists by developing physics-based and data-driven models of the human central nervous system under both physiological and pathological conditions. Through high-performance simulations, multiscale mechanisms and multiphysics processes that are difficult to measure in vivo can be investigated. Moreover, integrating clinical data into these models enables personalization, forming the foundation for digital twins that support diagnosis, treatment planning, and monitoring. Bringing these approaches into clinical practice is an interdisciplinary challenge that opens new opportunities in precision medicine. The proposed school aims to provide participants with a comprehensive introduction to the fundamental principles of mathematical multiscale and multiphysics models of nervous system function, as well as state-of-the-art methods for the numerical approximation of these complex models and data-driven strategies for model personalization from multi-modal data. In addition, medical doctors will share their clinical perspective and highlight the most pressing challenges encountered in patient care. The event is part of the activities of "Dipartimento di Eccellenza" - Line 2
- Monday, 11 October 2027 - Friday, 15 October 2027
  Lake Como School of Advanced Studies, Villa del Grumello
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568