Dipartimento di Matematica

Research - Laboratories - Teaching

Head of Dept: Prof.ssa Irene Maria Sabadini

Vice-Head of Dept: Prof. Emilio Barucci

Department Manager: Dr.ssa Franca Di Censo

NONLINEAR MEETING IN MILAN 2023
December 18-19, 2023
Christmas Workshop on Fluid Mechanics
December 19-21, 2023
ERC Synergy Grant 2023 awarded to Paola F. Antonietti
In collaboration with the co-PIs Lourenco Beirao da Veiga, Daniele A. Di Pietro, Jerome Droniou
more... The Mathematics Department of the Politecnico di Milano: Department of Excellence

MOX

Laboratory of Modeling
and
Scientific Computing

EFFEDIESSE

Laboratory of Mathematics Education
and
Scientific Experimentation

analysis@polimi

Research Group

QFINLAB

Quantitative Finance Lab

Department of Excellence

Upcoming Events

dec 11 mon 2023

MOX Seminar
Wietse Boon, Concluding the Project MiDiROM: Multipoint Mixed Finite Elements and Locally Conservative Deep Learning Methods for Porous Media Problems, 12-11-2023, 11:00

MOX Seminar
Wietse Boon
MOX, Dipartimento di Matematica, Politecnico di Milano
Concluding the Project MiDiROM: Multipoint Mixed Finite Elements and Locally Conservative Deep Learning Methods for Porous Media Problems
Monday, 11 December 2023 at 11:00
Aula Saleri
Abstract

We reflect on the MSCA-IF project MiDiROM, presenting its successes and challenges over the past two years, and discussing the remaining open questions. The project's main objective was to develop efficient computational methods for modeling processes in fractured porous media, by combining mixed-dimensional modeling with deep learning approaches.

This talk focuses on two prominent research themes within MiDiROM. Firstly, we developed multipoint mixed finite element methods for rotation-based formulations of Stokes flow and Biot poroelasticity. By using exact discrete complexes and a carefully selected quadrature rule, we obtained efficient and stable discretization methods using the lowest-order Raviart-Thomas finite element pair.
Secondly, we introduced reduced order modeling techniques for Darcy flow systems capable of generating locally mass conservative flux fields. These methods combine concepts from reduced basis methods, exact discrete complexes, and trained neural networks. Mass conservation is then guaranteed through a "spanning tree solve" and appropriate projection operators.

To conduct numerical simulations, we simultaneously developed the Python package PyGeoN, in which discrete complexes are explicitly available. The conclusion of the talk will emphasize various capabilities of this open-source software, such as mixed-dimensional differential operators and a polygonal mesh generator using aperiodic monotiles.

Contatto:
alessio.fumagalli@polimi.it
Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

dec 12 tue 2023

Seminar
Antonino De Martino, Spectral theories on the S-Spectrum, 12-12-2023, 15:15
- Seminar
- Antonino De Martino
- Politecnico di Milano
- Spectral theories on the S-Spectrum
- Tuesday, 12 December 2023 at 15:15
- Aula Seminari - III Piano
- Abstract
  
  One of the deepest results in hypercomplex analysis is the Fueter extension theorem. It gives a two steps procedure to extend holomorphic functions to the hyperholomorphic setting. The first step gives the class of slice hyperholomorphic functions; their Cauchy formula allows to define the so-called S-functional calculus for noncommuting operators based on the S-spectrum. In the second step, this extension procedure generates monogenic functions; the related monogenic functional calculus, based on the monogenic spectrum, was widely studied by McIntosh and collaborators.
  In this talk, I will discuss the main notions of the S-spectrum and some concepts of the monogenic functional calculus. Moreover, I will also give some ideas on the new research direction of the fine structures.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
dec 13 wed 2023

Seminar
Eugenia Taranto, Ricerca Operativa: attività di modellizzazione e problem-solving a scuola, 12-13-2023, 15:00
- Seminar
- Eugenia Taranto
- Università Kore di Enna
- Ricerca Operativa: attività di modellizzazione e problem-solving a scuola
- Wednesday, 13 December 2023 at 15:00
- Aula didattica FDS 4°piano - tiny.cc/zoomfds
- Abstract
  
  La ricerca operativa (RO) è una branca della matematica applicata solitamente insegnata a livello universitario. Tuttavia, negli ultimi anni sono state sviluppate diverse iniziative per introdurre la RO agli studenti delle scuole secondarie. A queste iniziative si aggiunge ROAR (Ricerca Operativa Applicazioni Reali), un corso triennale composto da tre unità didattiche, pensato per gli studenti del triennio delle scuole secondarie. In questo seminario ci si concentrerà sulla prima unità didattica, mettendo in luce sia gli aspetti contenutistici sia le metodologie utilizzate per la sua implementazione con gli studenti. In particolare, si delineeranno gli aspetti teorici che hanno guidato la progettazione e poi si mostreranno esempi di problemi di ottimizzazione proposti agli studenti, che mirano a sviluppare le loro capacità di modellizzazione e problem-solving.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
dec 14 thu 2023

Seminar
Massimiliano Alessandro, On the Classification of Surfaces of General Type with pg=q=2, 12-14-2023, 14:30 precise
- Seminar
- Massimiliano Alessandro
- Università di Genova e Universität Bayreuth
- On the Classification of Surfaces of General Type with pg=q=2
- Thursday, 14 December 2023 at 14:30 right
- Aula seminari III piano
- Abstract
  
  The classification of minimal surfaces of general type is a classical and long-standing research topic. In this context fixing invariants turns out to be fundamental.
  In this talk we will review some recent results on the case pg=q=2, which is still widely open in spite of several contributions by many authors over the last two decades. More specifically, given a minimal surface S of general type with pg=q=2, it turns out that the self-intersection K^2 of the canonical divisor K is 4
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
dec 18 mon 2023

dec 19 tue 2023

WorkShop
Nonlinear meeting in milan 2023
12/18/2023 - 12/19/2023
- WORKSHOP
- NLMM23
  Nonlinear meeting in milan 2023
- organizers
  Maurizio Garrione, Benedetta Noris
- Il Workshop si svolgerà su due mezze giornate e prevede conferenze tenute da: • Isabeau Birindelli (Sapienza Università di Roma) • Alberto Boscaggin (Università di Torino) • Mauro Garavello (Università di Milano-Bicocca) • Stefano Marò (Universidad de Oviedo) • Federica Sani (Università di Modena e Reggio Emilia) • Giusi Vaira (Università di Bari)
- Monday, 18 December 2023 - Tuesday, 19 December 2023
  Sala Consiglio, 7° piano, Dipartimento di Matematica, Ed.14, 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
dec 19 tue 2023

dec 21 thu 2023

WorkShop
Christmas workshop on fluid mechanics
12/19/2023 - 12/21/2023
- WORKSHOP
- Christmas workshop on fluid mechanics
- organizers
  Edoardo Bocchi, Alessio Falocchi, Filippo Gazzola, Andrea Giorgini, Gianmarco Sperone
- Tuesday, 19 December 2023 - Thursday, 21 December 2023
  Sala Consiglio, 7° piano, Dipartimento di Matematica, Ed.14, 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

jan 11 thu 2024

MOX Colloquia
Ramon Codina, Mixed finite element methods in Elasticity---inf-sup stability vs stabilisation, 01-11-2024, 14:00

MOX Colloquia
Ramon Codina
Universitat Politècnica de Catalunya
Mixed finite element methods in Elasticity---inf-sup stability vs stabilisation
Thursday, 11 January 2024 at 14:00
Aula Consiglio VII piano - Dipartimento di Matematica
Abstract

In this talk we consider the finite element approximation of some mixed formulations of linear elasticity, namely, the displacement-pressure, the displacement-stress and the displacement-pressure-stress approaches. As for any mixed formulation, involving unknowns belonging to different functional spaces, the global inf-sup stability that ensures well posedness of the problem is a consequence of “little” inf-sup conditions that need to be satisfied between the interpolating spaces of the different unknowns. Approximations satisfying these conditions are sometimes difficult to implement, and even very rare, as in the case of the displacement-pressure-stress approach. The alternative is to modify the discrete problem by adding stabilisation terms to the Galerkin equations that yield stable approximations for any choice of the interpolating spaces. We discuss this possibility and show that one may prove stability and convergence in the same norms as for the continuous problem.

Contatto: simona.perotto@polimi.it

Ramon Codina

Ramon Codina is Professor of Continuum Mechanics and Structural Analysis at the Technical University of Catalonia (UPC), where he began his academic career in 1990. He teaches courses on continuum mechanics and mechanics of structures, as well as courses on computational mechanics and functional analysis in mechanics.

His research is concerned with the development, implementation and numerical analysis of finite element methods applied to physical problems in engineering, mainly in fluid mechanics, but also in solids and electromagnetism. He is responsible for the research group Numerical Analysis and Computation, identified as a group of excellence by the Generalitat de Catalunya, and leader of the Fluid Mechanics Group at the International Centre for Numerical Methods in Engineering (CIMNE).

In recognition to his research, he has received several awards, among which the Prandtl Medal from Eccomas (2018), the ICREA Academia Award (2011, 2016 and 2021) from the Catalan Government, the IACM Young Investigator Award (2004), the JL Lions Award to Young Scientists in Computational Mathematics from Eccomas (2000) and the Distinció de la Generalitat de Catalunya per a la Recerca Universitària (2000).

Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

jan 17 wed 2024

Seminar
Filippo Gazzola, Un fallimento del calcolo vettoriale: le interazioni fluido-struttura, 01-17-2024, 15:00
- Seminar
- Filippo Gazzola
- Dipartimento di Matematica, Politecnico di Milano
- Un fallimento del calcolo vettoriale: le interazioni fluido-struttura
- Wednesday, 17 January 2024 at 15:00
- Aula didattica FDS 4°piano - tiny.cc/zoomfds
- Abstract
  
  Verranno osservati e discussi alcuni fenomeni di interazione fluido-struttura della vita quotidiana. I comportamenti sia dei fluidi che delle strutture sembrano mettere in discussione i principi elementari del calcolo vettoriale.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

jan 23 tue 2024

MOX Colloquia
David Keyes, Efficient Computation through Tuned Approximation, 01-23-2024, 14:00

MOX Colloquia
David Keyes
Extreme Computing Research Center at the King Abdullah University of Science and Technology (KAUST)
Efficient Computation through Tuned Approximation
Tuesday, 23 January 2024 at 14:00
Aula Consiglio VII piano - Dipartimento di Matematica
Abstract

Numerical software is being reinvented to provide opportunities to tune dynamically the accuracy of computation to the requirements of the application, resulting in savings of memory, time, and energy. Floating point computation in science and engineering has a history of “oversolving” relative to expectations for many models. So often are real datatypes defaulted to double precision that GPUs did not gain wide acceptance until they provided in hardware operations not required in their original domain of graphics. However, computational science is now reverting to employ lower precision arithmetic where possible. Many matrix operations considered at a blockwise level allow for lower precision and many blocks can be approximated with low rank near equivalents. This leads to smaller memory footprint, which implies higher residency on memory hierarchies, leading in turn to less time and energy spent on data copying, which may even dwarf the savings from fewer and cheaper flops. We provide examples from several application domains, including a look at entries that earned Gordon Bell Prize finalist status in 2022 and 2023.

Contatti:
alfio.quarteroni@polimi.it
paola.antonietti@polimi.it

David Keyes

David Keyes directs the Extreme Computing Research Center at the King Abdullah University of Science and Technology (KAUST), where he was a founding Dean in 2009 and currently serves in the Office of the President as Senior Associate. He is a professor in the programs of Applied Mathematics, Computer Science, and Mechanical Engineering. He is also an Adjunct Professor of Applied Mathematics and Applied Physics at Columbia University, where he formerly held the Fu Foundation Chair. He works at the interface between parallel computing and PDEs and statistics, with a focus on scalable algorithms that exploit data sparsity. Before joining KAUST, Keyes led multi-institutional scalable solver software projects in the SciDAC and ASCI programs of the US Department of Energy (DoE), ran university collaboration programs at US DoE and NASA institutes, and taught at Columbia, Old Dominion, and Yale Universities. He is a Fellow of SIAM, the AMS, and the AAAS. He has been awarded the Gordon Bell Prize from the ACM, the Sidney Fernbach Award from the IEEE Computer Society, and the SIAM Prize for Distinguished Service to the Profession. He earned a B.S.E. in Aerospace and Mechanical Sciences from Princeton in 1978 and a Ph.D. in Applied Mathematics from Harvard in 1984.

Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

jan 24 wed 2024

Seminar
Alessandra Mariotti, Argomentare in Matematica, 01-24-2024, 15:00
- Seminar
- Alessandra Mariotti
- Università di Siena
- Argomentare in Matematica
- Wednesday, 24 January 2024 at 15:00
- Aula didattica FDS 4°piano - tiny.cc/zoomfds
- Abstract
  
  Il tema dell'argomentazione, nella sua declinazione nei diversi ambiti disciplinari, è chiaramente espresso nelle indicazioni Nazionali, ma spesso disatteso nella pratica scolastica.
  Educare all'argomentazione presenta problemi didattici specifici che, nell'ambito matematico, si articolano con i problemi didattici relativi sia alla costruzione dei concetti che all'introduzione ad una prospettiva teorica, ed in particolare alla pratica della dimostrazione.
  Da qualche decennio la ricerca in didattica della matematica affronta i problemi che emergono in ambito scolastico in relazione all'argomentare, al dimostrare e al loro mutuo rapporto.
  Il seminario ha l'obiettivo di discutere alcuni di questi problemi didattici proponendo, alla luce dalla ricerca in questo ambito, qualche esempio di buone pratiche da sviluppare in classe.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

jan 25 thu 2024

MOX Colloquia
Sauro Succi, Towards Quantum Computing for Fluids, 01-25-2024, 14:00

MOX Colloquia
Sauro Succi
La Sapienza, Harvard University
Towards Quantum Computing for Fluids
Thursday, 25 January 2024 at 14:00
Aula Consiglio VII piano
Abstract

We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, such as quantum nonlinear ODE solvers, Carleman-Koopman linearization, functional Liouville formulations and variational quantum eigensolvers, will be briefly discussed and commented on. We shall then focus on two distinct quantum computing implementations of the Carleman-Koopman procedure, one based on quantum linear algebra solvers and the other on a second-quantized Dirac-Majorana formulation of the Lattice Boltzmann equation. Finally, we shall offer a brief mid-term perspective of quantum versus exascale computing for fluid flows.

Contatto: alfio.quarteroni@polimi.it

Sauro Succi

Sauro Succi serves as Senior Research Executive and Principal Investigator at the Center for Life Nano-Neuro Sciences at la Sapienza of the Italian Institute of Technology and Research Affiliate of the Physics Department of Harvard University. He holds a degree in nuclear engineering from the University of Bologna and a PhD in physics from EPFL. His research activity covers a broad range of topics related to the mathematical modeling and simulation of complex states of flowing matter, such as thermonuclear plasmas, fluid turbulence, soft matter as well as quantum and subnuclear fluids such as quark gluon plasmas. He is best known for his contributions to the early inception, development and application of the Lattice Boltzmann method, for which he has received a number of international awards, including the Alexander von Humboldt Award in Physics (2002), the Raman Chair of the Indian Academy of Sciences (2012), the APS Aneesur Rahman Prize in Computational Physics (2017), and the CECAM Berni Alder Prize (2019) for exceptional contributions to the microscopic simulation of matter. He is also a ERC Advanced Grant and PoC awardee (2017,2022), an elected member of Academia Europaea (2015) and a Honorary Professor at University College London (2022).

Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

jan 31 wed 2024

Seminar
Marco Pedroni, La catenaria, una corda che lega fisica, architettura, matematica e bolle di sapone, 01-31-2024, 15:00
- Seminar
- Marco Pedroni
- Dipartimento di Ingegneria gestionale, dell’informazione e della produzione, Università di Bergamo
- La catenaria, una corda che lega fisica, architettura, matematica e bolle di sapone
- Wednesday, 31 January 2024 at 15:00
- Aula didattica FDS 4°piano - tiny.cc/zoomfds
- Abstract
  
  Quale forma assume una catena omogenea appesa ai suoi estremi quando è sottoposta alla sola forza peso? Nel XVII secolo questa domanda ha impegnato le menti di grandi scienziati, che hanno individuato nella cosiddetta catenaria (una curva esprimibile in termini di funzioni iperboliche) la risposta. Per via di questa sua particolarità, essa è stata utilizzata in architettura, soprattutto da Antoni Gaudí. In questo seminario vedremo qualche esempio di questo utilizzo e mostreremo che la catenaria svolge un importante ruolo anche nella descrizione delle forme assunte dalle pellicole di acqua saponata.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
feb 14 wed 2024

Seminar
Andrea Gorini, L'introduzione della ''lettera'', dall'aritmetica all'algebra... e non solo, 02-14-2024, 15:00
- Seminar
- Andrea Gorini
- Scuola S. Girolamo Emiliani, Corbetta (MI), Associazione Ma.P.Es. Matematica - Pensiero - Esperienza
- L'introduzione della ''lettera'', dall'aritmetica all'algebra... e non solo
- Wednesday, 14 February 2024 at 15:00
- Aula didattica FDS 4°piano - tiny.cc/zoomfds
- Abstract
  
  L’introduzione del calcolo letterale nell’ultimo anno della scuola secondaria di primo grado spesso si rivela come il momento in cui si manifesta la distanza tra l’essere in grado di svolgere una procedura e l’averla compresa, e che in genere segna una svolta irreversibile verso l’abbandono di interesse e impegno da parte degli studenti. Una delle cause dell’insorgere di questa distanza è la relativa facilità d’uso del linguaggio algebrico e delle sue regole sintattiche, che rischia di oscurarne la profondità semantica. Nel seminario si intende proporre alcuni spunti di riflessione affinché l’introduzione della “lettera” sia un passaggio di maturazione nell’acquisizione del linguaggio della Matematica nella pienezza della sua potenzialità.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568