Dipartimento di Matematica

Ricerca - Laboratori - Formazione

Direttore: Prof.ssa Irene Maria Sabadini

Direttore Vicario: Prof. Emilio Barucci

Responsabile Gestionale: Dr.ssa Franca Di Censo

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Il Dipartimento di Matematica del Politecnico di Milano si è posizionato al 34 posto a livello mondiale per la Matematica nel prestigioso QS World University Rankings by Subject 2023, la graduatoria mondiale delle migliori università per ambito disciplinare. L'ottima posizione è stata raggiunta con un miglioramento di ben 25 posti rispetto al 2022. A livello nazionale, il Dipartimento si conferma, per la seconda volta consecutiva, al primo posto.

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Dipartimento d'eccellenza

Prossimi Eventi

giu 06 mar 2023

Seminar
Alberto Bressan, Optimal control of propagation fronts and moving sets, 06-06-2023, ore 16:30
- Seminar
- Alberto Bressan
- The Pennsylvania State University
- Optimal control of propagation fronts and moving sets
- Martedì 6 giugno 2023 alle ore 16:30
- Sala Consiglio 7^ piano, Dipartimento di Matematica ed. 14, Politecnico di Milano
- Abstract
  
  We consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population. A simpler model is then derived, describing the controlled evolution of a contaminated set.
  The first part of the talk will focus on the optimal control of 1-dimensional traveling wave profiles.
  Namely, we seek a control with minimum norm which produces a traveling profile with a given speed.
  In turn, this leads to a family of optimization problems for a moving set, related to the original reaction-diffusion equation via a sharp interface limit. In connection with moving sets, the second part of the talk will present some results on controllability, existence of optimal strategies, and optimality conditions. Some open questions will be discussed.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
giu 13 mar 2023

giu 15 gio 2023

Convegno
Summer school on advanced parallel-in-time methods
13/06/2023 - 15/06/2023
- CONVEGNO
- Summer school on advanced parallel-in-time methods
- organizzatori
  Gabriele Ciaramella
- The goal of this summer school is to introduce basic and advanced parallel-in-time methods to researchers interested in understanding these methods, and to give them detailed insight on how these methods reduce various error components and are used in practice. The course will cover parallel-in-time methods for various time-dependent problems ranging from parabolic and hyperbolic partial differential equations (PDEs) to PDE-constrained optimization problems. The school is suitable for young mathematicians (PhD students and highly motivated Master Students), who wish to either get in touch with parallel-in-time methods, as well as young researchers and Post-docs who desire to strengthen and broaden their knowledge on advanced time-parallelization techniques. The event is funded by the European Mathematical Society and the Indam GNCS group.
- Martedì 13 giugno 2023 - Giovedì 15 giugno 2023
  Sala del Consiglio
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
giu 13 mar 2023

Seminar
Alexander Volberg, Quantum learning via harmonic analysis on Boolean cube and cyclic groups, 13-06-2023, ore 16:30 precise
- Seminar
- Alexander Volberg
- Michigan State University
- Quantum learning via harmonic analysis on Boolean cube and cyclic groups
- Martedì 13 giugno 2023 alle ore 16:30 precise
- Sala di Rappresentanza, Dipartimento di Matematica, Università di Milano
- Abstract
  
  The interaction between learning theory and harmonic analysis was emphasized by mathematics of quantum computing. One of the outstanding open problems in this area concerns the Bohnenblust--Hille inequality
  that generalizes a celebrated Littlewood’s 4/3 lemma. How to learn (approximately and with large probability) a very large matrix in a relatively small number of random quantum quarries? Motivated by this question, a non-commutative counterpart of Bohnenblust--Hille inequality for Boolean cubes was recently conjectured in Cambyse Rouz, Melchior Wirth, and Haonan Zhang. By waving the hands I will explain the proof of non-commutative Bohnenblust--Hille inequalities with constants that are dimension-free. As applications, we study learning problems of quantum observables. Using Heisenberg—Weyl basis one
  reduces the quantum problem to commutative problem: the Bohnenblust—Hille inequality for cyclic groups (joint with Haonan Zhang, Joe Slote). To prove the Bohnenblust—Hille inequality for cyclic groups turned out to be a challenging problem. I will explain the progress in this area.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
giu 15 gio 2023

Seminar
Francesco Buscemi, The Theory of Statistical Comparison: From Majorization to the Quantum Blackwell Theorem and Beyond, 15-06-2023, ore 14:30 precise
- Seminar
- Francesco Buscemi
- Department of Mathematical Informatics, Nagoya University
- The Theory of Statistical Comparison: From Majorization to the Quantum Blackwell Theorem and Beyond
- Giovedì 15 giugno 2023 alle ore 14:30 precise
- Aula Seminari III piano
- Abstract
  
  For problems that allow statistical interpretation, such as parameter estimation or information transmission, whenever different strategies are possible, it is natural to compare them on the basis of their statistical performance with respect to the problem at hand. The theory of statistical comparison provides a rigorous formalization of this scenario. In this colloquium, I will introduce the basic ideas of the classical theory, including the theory of majorization and the Blackwell-Shermal-Stein theorem, present their extensions to the quantum setting, and discuss applications in quantum measurement theory and quantum statistical mechanics.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568
giu 21 mer 2023

Convegno
Numbers and stories new directions for climate storylines and scenarios
21/06/2023
- CONVEGNO
- Numbers and stories new directions for climate storylines and scenarios
- organizzatori
  Hernan Bobadilla (DMAT) Rawad El Skaf (DMAT) Francesco Nappo (DMAT) Massimo Tavoni (DIG) Giovanni Valente (DMAT)
- The aim of ''Numbers and Stories'' is to survey and discuss new directions in climate change research, with an interdisciplinary approach. The theme of the workshop revolves around the use of qualitative and quantitative methods in climate change research, most importantly the development and use of scenarios for emission and decarbonization pathways, the storyline approach to detection and attribution of extreme weather events, and their repercussions for climate policy under deep uncertainty. Scenarios are key tools for depicting future climate and play a key role in assessments such as those of the IPCC. As the community looks forward to developing the next generation of scenarios, it is important to discuss which elements should be included in the narrative and operationalized in the qualitative and quantitative assessments. The workshop is planned as a full-day event with individual talks on Storylines in the morning and Scenarios/Integrated Assessment Models (IAMs) in the afternoon. We will end with a panel discussion focused on the recent AR6 IPCC report with invited panelists, speakers and the organizing/scientific committee. ''Numbers and Storie'' is an in-person only event. Participation is free of charge. Registration is required.
- Mercoledì 21 giugno 2023 - Mercoledì 21 giugno 2023
  Room 16B.1.1 - PoliMi (Leonardo)
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

giu 22 gio 2023

MOX Colloquia
Giuseppe Savaré, Optimal transport and gradient flows: a brief overview, 22-06-2023, ore 14:00

MOX Colloquia
Giuseppe Savaré
Università Bocconi
Optimal transport and gradient flows: a brief overview
Giovedì 22 giugno 2023 alle ore 14:00
Aula Consiglio VII piano - Dipartimento di Matematica
Abstract

Optimal transport theory studies the optimal strategies for transferring a given initial distribution of resources (mathematically represented by a measure) to a final configuration in a way that minimizes the cost of transport.
First addressed mathematically by G. Monge in 1781, its first modern formulation (1942) earned L.V. Kantorovich the Nobel Prize in Economics in 1975.
Later, thanks to many outstanding theoretical, applied and numerical contributions, the theory has been developed in many directions including, in addition to economics, linear and stochastic programming, statistics and probability, mean field models, functional analysis, PDEs, Riemannian geometry, machine learning.
The seminar aims to give a quick overview of some of the classical results and more recent contributions, with applications to evolution problems.

Contatto: marco.verani@polimi.it

Giuseppe Savaré

Giuseppe Savaré started his scientific career as a researcher at the CNR Institute for Numerical Analysis in Pavia and has been Professor of Mathematical Analysis since 2000, first at the University of Pavia and then, since 2020, at Bocconi University in Milan.
During 2019-2023 he was Hans-Fischer Senior Fellow at the Institute for Advanced Study of the Technical University of Munich. In 2011 he received the Ennio De Giorgi prize awarded by the Italian Mathematical Union.
His research activity concerns variational methods for evolution problems, in particular gradient flows and rate-independent models, and their interplay with optimal transport, measure theoretic tools and analysis in metric spaces.
In collaboration with Luigi Ambrosio and Nicola Gigli, he has written a monograph on Gradient Flows in Metric Spaces and in the Space of Probability Measures.

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

giu 28 mer 2023

MOX Seminar
Paolo Piersanti, On the justification of Koiter's model for linearly elastic shells confined in a half-space. Theory and Numerical Analysis., 28-06-2023, ore 14:00

MOX Seminar
Paolo Piersanti
Indiana University
On the justification of Koiter's model for linearly elastic shells confined in a half-space. Theory and Numerical Analysis.
Mercoledì 28 giugno 2023 alle ore 14:00
Aula Saleri
Abstract

In this talk, we will review some recent results on the modelling, analysis and numerical analysis of Koiter’s model for linearly elastic shells in the case where the shell under consideration is constrained to remain confined in a prescribed half-space.

To begin with, we will see how to recover the constrained Koiter’s model starting from the classical three-dimensional equations of linearized elasticity in the case where the shell under consideration is an elliptic membrane or a flexural shell.

Contatti: paola.antonietti@polimi.it e vittorino.pata@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

giu 29 gio 2023

Seminar
Luigi Berselli, Energy conservation or anomalous dissipation for incompressible fluids, 29-06-2023, ore 15:15
- Seminar
- Luigi Berselli
- Università di Pisa
- Energy conservation or anomalous dissipation for incompressible fluids
- Giovedì 29 giugno 2023 alle ore 15:15
- Aula Seminari III piano
- Abstract
  
  We provide an overview and propose elementary proofs of energy conservation for weak solutions to the Euler and Navier-Stokes
  equations in the class of Holder continuous functions. Our focus is on exploring the interplay between space and time regularity.
  
  Additionally, we delve into the potential extension of these results to the Navier-Stokes equations in the presence of a solid boundary. Specifically, we consider the case of Dirichlet boundary conditions and our approach avoids any additional assumptions on the kinematic pressure.
- Politecnico di Milano, Dipartimento di Matematica edificio 14, via E. Bonardi 9, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

lug 14 ven 2023

MOX Seminar
Elena Gaburro, Structure preserving high order Lagrangian schemes for the solution of hyperbolic equations: from fluid-dynamics to astrophysics, 14-07-2023, ore 14:30

MOX Seminar
Elena Gaburro
Inria center Bordeaux-Sud-Ouest, France
Structure preserving high order Lagrangian schemes for the solution of hyperbolic equations: from fluid-dynamics to astrophysics
Venerdì 14 luglio 2023 alle ore 14:30
Aula Saleri
Abstract

In this talk we present a novel family of high order accurate numerical schemes for the solution of hyperbolic partial differential equations (PDEs) which combines several geometrical and physical structure preserving properties.

Indeed, first, we settle in the Lagrangian framework, where each element of the mesh evolves following as close as possible the local fluid flow, so to reduce the numerical dissipation at contact waves and moving interfaces and to respect the Galilean and rotational invariance of the studied PDEs system. In particular, we choose the direct Arbitrary-Lagrangian-Eulerian setting which, in order to always guarantee the high quality of the moving mesh, allows to combine the Lagrangian motion with mesh optimization techniques.
The employed Voronoi tessellation is thus regenerated at each time step, the previous one is connected with the new one by space-time control volumes, including hole-like sliver elements in correspondence of topology changes, over which we integrate a space-time divergence form of the original PDEs through a high order accurate ADER discontinuous Galerkin (DG) scheme. Mass conservation and the respect of the GCL condition are guaranteed by construction thanks to the integration over closed control volumes, and robustness over shock discontinuities is ensured by the use of an a posteriori sub-cell finite volume (FV) limiter. On the top of this effective moving mesh framework, we have also made, for the first time in literature, the full ALE ADER DG scheme with a posteriori sub-cell FV limiter well balanced in order to increase our resolution on small perturbations of equilibrium solutions.

The presentation is closed by a wide set of numerical results, including simulations of Keplerian disks, which demonstrate all the claimed properties and the increased accuracy and robustness of our novel family of schemes. We will also give an outlook on future works on the Einstein field equations, based on our recent results obtained with Cartesian methods.

Acknowledgement:

E. Gaburro gratefully acknowledges the support received from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement SuPerMan (No. 101025563).

Contatti: luca.formaggia@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

ago 13 dom 2023

ago 18 ven 2023

Convegno
Summer school on higher structures in algebra and geometry
13/08/2023 - 18/08/2023
- CONVEGNO
- Summer school on higher structures in algebra and geometry
- organizzatori
  Andreas Hochenegger, Karin M. Jacobsen, David Ploog
- This school links three different areas, namely representation theory, symplectic geometry and algebraic geometry, using categorical approaches and higher structures in algebra. The target audience are categorically inclined PhD students and post-docs familiar with at least one of these fields, who want to broaden their vision of neighbouring areas.
- Domenica 13 agosto 2023 - Venerdì 18 agosto 2023
  Sophus Lie Conference Center, Nordfjordeid, Norway
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568