Dipartimento di Matematica

Research - Laboratories - Teaching

Head of Dept: Prof. Giulio Magli

Vice-Head of Dept: Prof. Gabriele Grillo

Department Manager: Dr.ssa Franca Di Censo

Polytopal Element Methods in Mathematics and Engineering
December 12-14, 2022
Geometric Analysis and PDEs at PoliMi
Energy Finance Italia 8 Conference
February 8-10 2023

MOX

Laboratory of Modeling
and
Scientific Computing

EFFEDIESSE

Laboratory of Mathematics Education
and
Scientific Experimentation

analysis@polimi

Research Group

QFINLAB

Quantitative Finance Lab

About us...

Today's events 05 dicembre 2022

dec 05 mon 2022

WorkShop
Geometric analysis and pdes at polimi
12/05/2022
- WORKSHOP
- Geometric analysis and pdes at polimi
- organizers
  Giulia Meglioli, Alberto Roncoroni
- Speakers: Alessandro AUDRITO (ETH Zürich) Stefano BORGHINI (Università di Milano-Bicocca) Mattia FOGAGNOLO (Università di Padova) Luciano MARI (Università di Torino) Paolo MASTROLIA (Università di Milano) Gloria PAOLI (Friedrich-Alexander Universität) Troy PETITT (Politecnico di Milano) Giacomo SODINI (Universität Wien)
- Monday, 5 December 2022 - Monday, 5 December 2022
  Aula Consiglio, VII piano (morning session) and Aula Seminari, VI piano (afternoon session)
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
dec 05 mon 2022

Seminar
Davide Fermi, Vacuum fluctuations with zero-range potentials, 12-05-2022, 11:15 precise
- Seminar
- Davide Fermi
- Politecnico di Milano
- Vacuum fluctuations with zero-range potentials
- Monday, 5 December 2022 at 11:15 right
- Aula Seminario VI piano
- Abstract
  
  The Casimir effect is a manifestation of van der Waals polarization forces acting between atoms and molecules, in a regime where relativistic retardation effects cannot be neglected. An effective description can be given in terms of quantum fields influenced by classical objects,
  such as boundaries or external potentials. This leads to the emergence of ultraviolet divergences which can be treated by means of the so-called zeta-function regularization. In this seminar I first present a rigorous implementation of the zeta-function technique, using the language of canonical quantization for a scalar field. To this purpose, complex powers of the elliptic operator describing the dynamics are used to define smeared versions of the Wightman field and renormalization of expectation values is ultimately attained by analytic continuation. Next, I address the issue of boundary anomalies, discussing some explicitly solvable models with zero-range potentials modeling semi-transparent walls.
  Based on joint works with Livio Pizzocchero (University of Milano).
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

dec 05 mon 2022

MOX Colloquia
Petros Koumoutsakos, AI\Computing: Alloys for flow modeling and control, 12-05-2022, 14:00

MOX Colloquia
Petros Koumoutsakos
ETH Zürich & Harvard University, Cambridge, MA, USA
AI\Computing: Alloys for flow modeling and control
Monday, 5 December 2022 at 14:00
Aula Consiglio VII piano - Dipartimento di Matematica
Abstract

Over the last thirty years, we have experienced more than a billion-fold increase in hardware capabilities and a dizzying pace of acquiring and transmitting massive amounts of data. Artificial Intelligence (AI) has been the beneficiaries of these advances, and today it is increasingly embedded in technologies that touch every aspect of humanity. However, along with the abundance of promise, there is an ever increasing amount of hype, in particular regarding the capabilities of learning algorithms to model, predict and control complex fluid mechanics problems.
In this talk, I will offer a perspective on forming alloys of AI and simulations for the prediction and control of complex flow systems. I will present novel algorithms for learning the Effective Dynamics (LED) of complex flows and a fusion of multi-agent reinforcement learning and scientific computing (SciMARL) for modeling and control of complex flow-structure interactions. I will juxtapose successes and failures and argue that the proper fusion of fluid mechanics knowledge and AI expertise are essential to advance scientific frontiers.

Contatto: alfio.quarteroni@polimi.it

Petros Koumoutsakos

Petros Koumoutsakos is Herbert S. Winokur, Jr., Professor of Engineering and Applied Sciences and Area Chair for Applied Mathematics at Harvard’s John A. Paulson School of Engineering and Applied Sciences (SEAS). He studied Naval Architecture (Diploma-NTU of Athens, M.Eng.-U. of Michigan), Aeronautics, and Applied Mathematics (PhD-Caltech) and has served as the Chair of Computational Science at ETH Zurich (1997-2020). Petros is elected Fellow of the American Society of Mechanical Engineers (ASME), the American Physical Society (APS), and the Society of Industrial and Applied Mathematics (SIAM). He is the recipient of the Advanced Investigator Award by the European Research Council and the ACM Gordon Bell prize in Supercomputing. He is elected International Member of the US National Academy of Engineering (NAE). His research interests are on the fundamentals and applications of computing and artificial intelligence to understand, predict and optimize fluid flows in engineering, nanotechnology, and medicine.

Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

Upcoming Events

dec 06 tue 2022

Seminar
Silvio Vismara, ESG and Crowdfunding Platforms, 12-06-2022, 10:00
- Seminar
- Silvio Vismara
- Università di Bergamo
- ESG and Crowdfunding Platforms
- Tuesday, 6 December 2022 at 10:00
- Aula Seminari III piano
- Abstract
  
  Environmental, social, and governance (ESG) factors have acquired great relevance for investors in recent years. This paper examines the intersection between ESG and crowdfunding, one of the most popular types of fintech. Using data on the population of 508 platforms established in the 37 OECD countries between 2007 and 2020, we document that platforms with higher levels of ESG criteria are more likely to survive over time. Results are robust to different measures of ESG and endogeneity concerns. The importance of ESG criteria depends on cultural differences, as it is more pronounced for those platforms operating in countries where the level of power distance is lower.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
dec 12 mon 2022

MOX Seminar
Giuseppe Romano, Inverse Design for Nanoscale Heat Transport, 12-12-2022, 15:30
- MOX Seminar
- Giuseppe Romano
- Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology (MIT), Cambridge, MA,
- Inverse Design for Nanoscale Heat Transport
- Monday, 12 December 2022 at 15:30
- On-line
- Abstract
  
  How to identify the geometry of a nanostructure given the desired effective thermal conductivity tensor? While several topology optimization methods have been developed for macroscale scenarios, they can’t be readily applied to nanoscale devices. In fact, when the feature size of the material becomes comparable with the particles’ mean-free path, flux becomes nondiffusive, and a momentum-resolved model is needed. On the other side, standard material interpolation methods, such as SIMP, are mostly applied to averaged quantities, such as the local thermal conductivity. In this talk, I will discuss our recent attempt at solving this issue [1], based on a novel method, termed the “Transmission Interpolation Method” (TIM). Instead of working with locally resolved variables, TIM acts on the interfacial phonon flux and links it to the material distribution. The talk will show the application of this approach to two examples: Tuning the effective thermal conductivity tensor of a nanostructure and maximizing phonon size effects. The talk will conclude with a demo and remarks for future developments.
  [1] Giuseppe Romano and Steven G Johnson, Structural and Multidisciplinary Optimization 65, 297 (2022)
  
  Contatto: giulia.pozzi@polimi.it
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
dec 14 wed 2022

Seminar
Chiara Andrà, Rosa Iaderosa, Rappresentazioni e problem-solving, 12-14-2022, 15:00
- Seminar
- Chiara Andrà, Rosa Iaderosa
- Università del Piemonte Orientale, Rally Matematico Transalpino
- Rappresentazioni e problem-solving
- Wednesday, 14 December 2022 at 15:00
- Aula seminari VI piano
- Abstract
  
  Il seminario si propone di analizzare rappresentazioni esterne spontanee o indotte messe in atto da studenti durante la risoluzione di problemi. Le rappresentazioni esterne possono fare da ponte per l’elaborazione di una strategia risolutiva. A volte si trovano schemi personali che riflettono il processo di pensiero utilizzato. Spesso esse sostituiscono anche un’esplicitazione verbale del processo risolutivo, o comunque coesistono con questa in un intreccio tra registro verbale e iconico, o grafico-simbolico. Durante il seminario saranno analizzate le risposte degli studenti con lo scopo di fornire indicazioni didattiche durante attività di problem-solving.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
dec 15 thu 2022

MOX Seminar
Antonia Larese, The Material Point Method for the simulation of water-related hazards and their interaction with critical structures, 12-15-2022, 10:00
- MOX Seminar
- Antonia Larese
- Universita degli studi di Padova & Technical University of Munich
- The Material Point Method for the simulation of water-related hazards and their interaction with critical structures
- Thursday, 15 December 2022 at 10:00
- Aula Consiglio VII piano - Dip. Matematica
- Abstract
  
  In recent years, natural hazards involving large mass movements such as landslides, debris flows, and mud flows have been increasing their frequency and intensity as a consequence of climate change and other related factors. These phenomena often carry huge rocks and heavy materials that may, directly or indirectly, cause damage to our structures resulting in a relevant socio-economic impact.
  The numerical simulation of the above events still represents a big challenge mainly for two reasons: the need to deal with large strain regimes and the intrinsic multiphysics nature of such events.
  While the Finite Element Method (FEM) represents a recognized, well established and widely used technique in many engineering fields, unfortunately it shows some limitation when dealing with problems where large deformation occurs. In the last decades many possible alternatives have been proposed and developed to overcome this drawback, such as the use of the so called particle-based methods. Among these, the Material Point Method (MPM) blends the advantages of both mesh-based and mesh-less methods. MPM avoids the problems of mesh tangling while preserving the accuracy of Lagrangian FEM and it is especially suited for non linear problems in solid mechanics and fluid dynamics.
  The talk will show some recent advances in MPM formulations [1], presenting both an irreducible and mixed formulation stabilized using variational multiscale techniques, as well as the partitioned strategies to couple MPM with other techniques such as FEM or DEM [2, 3]. All algorithms are implemented within the Kratos-Multiphysics open-source framework and available under the BSD license.
  References
  [1] Iaconeta, I., Larese, A., Rossi, R. and Guo, Z., Comparison of a Material Point Method and
  a Meshfree Galerkin Method for the simulation of cohesive-frictional materials, Materials, 10 , 1150, (2017).
  [2] Chandra, B., Singer, V., Teschemacher, T., Wuechner, R. and Larese, A., Nonconforming
  Dirichlet boundary conditions in Implicit Material Point Method by means of penalty augmentation,
  Acta Geotechnica, 16(8), 2315-2335 (2021).
  [3] Singer, V., Sautter, K.B., Larese, A., Wuchner, R. and Bletzinger, K.U.,, A Partitioned
  Material Point Method and Discrete Element Method Coupling Scheme , Under revision in Advanced Modeling and Simulation in Engineering Sciences (2022).
  Contatto: anna.scotti@polimi.it
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
dec 15 thu 2022

Seminar
Vincenzo De Risi, Diagrammi geometrici e teoria dello spazio dall'antichità all'età moderna, 12-15-2022, 17:00
- Seminar
- Vincenzo De Risi
- CNRS Université de Paris; Max Planck Institute
- Diagrammi geometrici e teoria dello spazio dall'antichità all'età moderna
- Thursday, 15 December 2022 at 17:00
- Sala di Rappresentanza del Dip. di Matematica, via C. Saldini 50
- Abstract
  
  Il seminario prende in considerazione il ragionamento diagrammatico in geometria elementare e le sue origini nella pratica matematica greca. Si discutono alcuni limiti ed alcune potenzialità di questo approccio ala geometria. Si mostra che il ruolo delle inferenze diagrammatiche diminuì nel corso della storia della geometria moderna anche prima di arrivare alla matematica astratta del diciannovesimo secolo. Le ragioni dell'abbandono delle pratiche diagrammatiche sembra legato alla trasformazione della geometria da una scienza delle figure in una scienza dello spazio. Si mostra allora che tale trasformazione ha preceduto e reso possibile la nascita della matematica astratta e di un ideale dimostrativo non-diagrammatico.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
jan 12 thu 2023

MOX Seminar
Daniele Avitabile, Uncertainty Quantification for spatially-extended neurobiological networks, 01-12-2023, 15:00
- MOX Seminar
- Daniele Avitabile
- VU-Amsterdam
- Uncertainty Quantification for spatially-extended neurobiological networks
- Thursday, 12 January 2023 at 15:00
- Aula Saleri VI piano - Dipartimento di Matematica
- Abstract
  
  This talk presents a framework for forward uncertainty quantification problems in spatially-extended neurobiological networks. We will consider networks in which the cortex is represented as a continuum domain, and local neuronal activity evolves according to an integro-differential equation, collecting inputs nonlocally, from the whole cortex. These models are sometimes referred to as neural field equations.
  Large-scale brain simulations of such models are currently performed heuristically, and the numerical analysis of these problems is largely unexplored. In the first part of the talk I will summarise recent developments for the rigorous numerical analysis of projection schemes [1] for deterministic neural fields, which sets the foundation for developing Finite-Element and Spectral schemes for large-scale problems.
  The second part of the talk will discuss the case of systems in the presence of uncertainties modelled with random data, in particular: random synaptic connections, external stimuli, neuronal firing rates, and initial conditions (and any combination thereof). Such problems give rise to random solutions, whose mean, variance, or other quantities of interest have to be estimated using numerical simulations. This so-called forward uncertainty quantification problem is challenging because it couples spatially nonlocal, nonlinear problems to large-dimensional random data.
  I will present a family of schemes that couple a spatial projector for the spatial discretisation, to stochastic collocation for the random data. We will analyse the time-dependent problem with random data and the schemes from a functional analytic viewpoint, and show that the proposed methods can achieve spectral accuracy, provided the random data is sufficiently regular.
  Acknowledgements. This talk presents joint work with Francesca Cavallini (VU Amsterdam), Svetlana Dubinkina (VU Amsterdam), and Gabriel Lord (Radboud University).
  References
  [1] Avitabile D, Projection methods for Neural Field Equations arXiv e-prints,
  arXiv:2112.03244 doi.org/10.48550/arXiv.2112.03244
  
  Contatto: simona.perotto@polimi.it
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
jan 18 wed 2023

Seminar
Orazio Puglisi, Paradossi dei sistemi elettorali, 01-18-2023, 15:00
- Seminar
- Orazio Puglisi
- Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze
- Paradossi dei sistemi elettorali
- Wednesday, 18 January 2023 at 15:00
- Sala Consiglio VII piano
- Abstract
  
  L’idea di “democrazia” che è ormai ben radicata dentro ciascuno di noi, spesso ci porta a considerare la questione dei sistemi elettorali (ovvero metodi per ottenere, a partire dalle preferenze degli individui di una certa popolazione, una lista di preferenze unica) con una certa leggerezza. Invece, appena si approfondisce la teoria dei sistemi di voto, ci si imbatte immediatamente in situazioni paradossali e problemi imprevisti, quasi sempre di difficile soluzione. Inizieremo questa conferenza discutendo alcuni dei principali problemi e paradossi che si presentano nella progettazione di un sistema elettorale. Nella parte finale ci occuperemo di un problema di diversa natura, ma di notevole importanza, ovvero quello della definizione “imparziale” dei collegi elettorali.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
feb 01 wed 2023

Seminar
Marco Beghi, La rivoluzione cosmologica del XVI-XVIII secolo: tempi e modi della sua affermazione, 02-01-2023, 15:00
- Seminar
- Marco Beghi
- Dipartimento di Energia, Politecnico di Milano
- La rivoluzione cosmologica del XVI-XVIII secolo: tempi e modi della sua affermazione
- Wednesday, 1 February 2023 at 15:00
- Sala Consiglio VII piano
- Abstract
  
  Tra il XVI e il XVIII secolo è avvenuta, in Europa, una rivoluzione cosmologica. Si tratta di molto più di un semplice cambiamento “geometrico” (il Sole al centro invece della Terra al centro); si tratta della sostituzione di tutto un insieme di conoscenze e di concezioni. Le nuove concezioni sono state sviluppate in modo non sincrono, talvolta secondo le osservazioni empiriche ma talvolta anche contro le osservazioni empiriche, e hanno preso il sopravvento quando sono arrivate a costituire un insieme sufficientemente completo e coerente.
  
  Vengono percorsi i passaggi principali, attraverso i protagonisti chiave (Copernico, Tycho Brahe, Keplero, Galileo, Newton), sia astronomi osservatori sia puramente speculativi, le loro scoperte e i loro tentativi di interpretazione, cercando di mettere in luce alcuni snodi che sono particolarmente interessanti dal punto di vista epistemologico.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
feb 15 wed 2023

Seminar
Alberto Saracco, “A cosa serve la matematica?” e altre domande che sente ogni insegnante., 02-15-2023, 15:00
- Seminar
- Alberto Saracco
- Dipartimento di Scienze matematiche, fisiche e informatiche; Università di Parma
- “A cosa serve la matematica?” e altre domande che sente ogni insegnante.
- Wednesday, 15 February 2023 at 15:00
- Sala Consiglio VII piano
- Abstract
  
  “A cosa serve la matematica?” Qual è quel docente che non si è mai sentito rivolgere questa domanda? Spesso è una domanda provocatoria, posta dallo studente più "simpatico" della classe. Ma a volte è una domanda sincera, posta da uno sconosciuto in treno. Solitamente siamo troppo stanchi o demoralizzati per rispondere a questa domanda. Ovviamente la matematica è utilissima, nel mondo di oggi, pieno di dati e in cui ogni aspetto della vita è intrecciato ad applicazioni, banali o profonde della matematica. Forse però vale la pena di soffermarsi un attimo in più su tale domanda e cercare di sviscerarla meglio...
  Cosa vuol dire "a cosa serve la matematica?"?
  La matematica pura è utile?
  Perché i politici devono sapere la matematica?
  A cosa serve a me la matematica?
  L'utilità della matematica è interessante per chi la studia?
  Nel seminario più che fornire le mie personali risposte proverò a dare un po' di materiale per pensarci su. Spero possa essere utile per avere qualche idea in più la prossima volta che sentirete queste o altre domande...
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

feb 23 thu 2023

MOX Colloquia
Nick Trefethen, Applications of AAA rational approximation, 02-23-2023, 14:00

MOX Colloquia
Nick Trefethen
University of Oxford
Applications of AAA rational approximation
Thursday, 23 February 2023 at 14:00
Aula Consiglio VII piano - Dipartimento di Matematica
Abstract

For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, including
* detection of singularities
* model order reduction
* analytic continuation
* functions of matrices
* nonlinear eigenvalue problems
* interpolation of equispaced data
* smooth extension of multivariate real functions
* extrapolation of ODE and PDE solutions into the complex plane
* solution of Laplace problems
* conformal mapping
* Wiener-Hopf factorization

(joint work with Stefano Costa and others)

Contatto: paola.antonietti@polimi.it

Nick Trefethen

Nick Trefethen is Professor of Numerical Analysis and head of the Numerical Analysis Group at Oxford University. He was educated at Harvard and Stanford and held positions at NYU, MIT, and Cornell before moving to Oxford in 1997. He is a Fellow of the Royal Society and a member of the US National Academy of Engineering, and served during 2011-2012 as President of SIAM. He has won many prizes including the Gold Medal of the Institute for Mathematics and its Applications, the Naylor Prize of the London Mathematical Society, and the Polya and von Neumann Prizes from SIAM. He holds honorary doctorates from the University of Fribourg and Stellenbosch University.
As an author Trefethen is known for his books including Numerical Linear Algebra (1997), Spectral Methods in MATLAB (2000), Spectra and Pseudospectra (2005), Approximation Theory and Approximation Practice (2013/2019), Exploring ODEs (2018), and An Applied Mathematician's Apology (2022). He organized the SIAM 100-Dollar, 100-Digit Challenge in 2002 and is the inventor of Chebfun.

Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568