Dipartimento di Matematica

Ricerca - Laboratori - Formazione

Direttore: Prof. Giulio Magli

Direttore Vicario: Prof. Gabriele Grillo

Responsabile Gestionale: Dr.ssa Franca Di Censo

Quantum before Christmas
December 20-22, 2021
Seminari EFFEDIESSE
a.a. 2021/2022
2-3 dicembre 2021
Sala Consiglio - 7° piano

MOX

Laboratorio di Modellistica
e
Calcolo Scientifico

EFFEDIESSE

Laboratorio di Formazione
e
Sperimentazione Didattica

analysis@polimi

Research Group

QFINLAB

Laboratorio di Finanza Quantitativa

Dicono di noi...

Prossimi Eventi

nov 29 lun 2021

Seminar
Marcello Porta, Correlation energy of mean-field Fermi gases, 29-11-2021, ore 14:00 precise
- Seminar
- Marcello Porta
- SISSA Trieste
- Correlation energy of mean-field Fermi gases
- Lunedì 29 novembre 2021 alle ore 14:00 precise
- Aula Seminario III Piano - Dipartimento di Matematica, Politecnico di Milano
- Abstract
  
  In this talk I will discuss the ground state properties of homogeneous, interacting Fermi gases, in the mean-field scaling. In this regime, Hartree-Fock theory provides a good approximation for the ground state energy of the system; this approximation is based on the replacement of the space of fermionic wave functions with the smaller set of Slater determinants, where the only correlations among the particles are those induced by the Pauli principle. I will discuss a rigorous approach that allows to go beyond the Hartree-Fock approximation, and that in particular allows to compute the leading order of the correlation energy, defined as the difference between the many-body and Hartree-Fock ground state energies. The expression we obtain reproduces the ground state energy of a non-interacting Bose gas, and agrees with the prediction of the random-phase approximation. The proof is based on a rigorous bosonization method, that allows to describe the particle-hole excitations around the Fermi surface in terms of a quasi-free Bose gas. Joint work with N. Benedikter, P. T. Nam, B. Schlein and R. Seiringer.
- 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
nov 30 mar 2021

Seminar
Elisa Sovrano, Sign-indefinite logistic growth models with flux-saturated diffusion, 30-11-2021, ore 15:15
- Seminar
- Elisa Sovrano
- Università degli Studi di Modena e Reggio Emilia
- Sign-indefinite logistic growth models with flux-saturated diffusion
- Martedì 30 novembre 2021 alle ore 15:15
- Aula Seminari III Piano
- Abstract
  
  Reaction-diffusion processes can be based on Fick-Fourier's law. Changing perspective, we deal with a dispersive flux which is a nonlinear bounded function of the gradient. In a bounded domain with a regular boundary, we investigate a Dirichlet problem associated with a quasilinear reaction-diffusion equation where the mean curvature operator drives the diffusion process. As for the reaction, we consider the product of a logistic-type nonlinearity and a sign-indefinite weight function modeling spatial heterogeneities. For this problem, we present some recent results concerning the existence and the multiplicity of positive solutions. Depending on the logistic term's behavior at zero, we prove three qualitatively different bifurcation diagrams by varying the diffusivity parameter. We point out a new multiplicity phenomenon without any similarity with the case of linear-diffusion logistic-growth models. This talk is based on joint works with Pierpaolo Omari (University of Trieste).
- 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

dic 01 mer 2021

Seminar
Leonardo Colzani, “DE NEXU INTER MULTITUDINEM CLASSIUM, IN QUAS FORMAE BINARIAE SECUNDI GRADUS DISTRIBUUNTUR, EARUMQUE DETERMINANTEM'' (GAUSS 1834), 01-12-2021, ore 15:00

Seminar
Leonardo Colzani
Università di Milano Bicocca
“DE NEXU INTER MULTITUDINEM CLASSIUM, IN QUAS FORMAE BINARIAE SECUNDI GRADUS DISTRIBUUNTUR, EARUMQUE DETERMINANTEM'' (GAUSS 1834)
Mercoledì 1 dicembre 2021 alle ore 15:00
online tiny.cc/fds22webex
Abstract

Nonostante il titolo, il seminario sarà elementare. Si parlerà del problema di contare il numero di punti a coordinate intere in una regione nel piano o nello spazio, un problema non banale con molte applicazioni.
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

dic 02 gio 2021

dic 03 ven 2021

Convegno
Recent advances in analysis, pdes and applications
02/12/2021 - 03/12/2021
- CONVEGNO
- Recent advances in analysis, pdes and applications
- organizzatori
  G. Meglioli, M. Muratori, C. Patriarca, F. Punzo
- Giovedì 2 dicembre 2021 - Venerdì 3 dicembre 2021
  Sala Consiglio - 7° piano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
dic 02 gio 2021

Seminar
Carrillo José Antonio, Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications, 02-12-2021, ore 17:00
- Seminar
- Carrillo José Antonio
- University of Oxford
- Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications
- Giovedì 2 dicembre 2021 alle ore 17:00
- On line
- Abstract
  
  This talk will be devoted to an overview of recent results understanding the bifurcation analysis of nonlinear Fokker-Planck equations arising in a myriad of applications such as consensus formation, optimization, granular media, swarming behavior, opinion dynamics and financial mathematics to name a few. We will present several results related to localized Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear diffusion Keller-Segel type models in several settings. We will show the existence of continuous or discontinuous phase transitions on the torus under suitable assumptions on the Fourier modes of the interaction potential. The analysis is based on linear stability in the right functional space associated to the regularity of the problem at hand. While in the case of linear diffusion, one can work in the L2 framework, nonlinear diffusion needs the stronger Linfty topology to proceed with the analysis based on Crandall-Rabinowitz bifurcation analysis applied to the variation of the entropy functional. Explicit examples show that the global bifurcation branches can be very complicated. Stability of the solutions will be discussed based on numerical simulations with fully explicit energy decaying finite volume schemes specifically tailored to the gradient flow structure of these problems. The theoretical analysis of the asymptotic stability of the different branches of solutions is a challenging open problem. This overview talk is based on several works in collaboration with R. Bailo, A. Barbaro, J. A. Canizo, X. Chen, P. Degond, R. Gvalani, J. Hu, G. Pavliotis, A. Schlichting, Q. Wang, Z. Wang, and L. Zhang. This research has been funded by EPSRC EP/P031587/1 and ERC Advanced Grant Nonlocal-CPD 883363.
- 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
dic 14 mar 2021

MOX Seminar
Mattia Serra, A mechanochemical instability drives vertebrate gastrulation, 14-12-2021, ore 14:30
- MOX Seminar
- Mattia Serra
- University of California, San Diego
- A mechanochemical instability drives vertebrate gastrulation
- Martedì 14 dicembre 2021 alle ore 14:30
- Live: Aula Consiglio, VII piano, Dip. di Matematica
  Online: mox.polimi.it/mox-seminars/?id_evento=2101
- Abstract
  
  Gastrulation is a critical event in vertebrate morphogenesis, characterized by coordinated large-scale multi-cellular movements. One grand challenge in modern biology is understanding how spatio-temporal morphological structures emerge from cellular processes in a developing organism and vary across vertebrates. We derive a theoretical framework that couples tissue flows, stress-dependent myosin activity, and actomyosin cable orientation. Our model, consisting of a set of nonlinear coupled PDEs, predicts the onset and development of observed experimental patterns of wild-type and perturbations of chick gastrulation as a spontaneous instability of a uniform state. We use analysis and numerics to show how our model recapitulates the phase space of gastrulation morphologies seen across vertebrates, consistent with experiments. Altogether, this suggests that early embryonic self-organization follows from a minimal predictive theory of active mechano-sensitive flows. www.biorxiv.org/content/10.1101/2021.10.03.462928v2
  
  Contatto: pasquale.ciarletta@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
dic 15 mer 2021

Seminar
Francesco Nappo, Modelli nella scienza e nella pedagogia scientifica: il caso di J. Clerk Maxwell, 15-12-2021, ore 15:00
- Seminar
- Francesco Nappo
- Politecnico di Milano
- Modelli nella scienza e nella pedagogia scientifica: il caso di J. Clerk Maxwell
- Mercoledì 15 dicembre 2021 alle ore 15:00
- online tiny.cc/fds22webex
- Abstract
  
  Utilizzeremo il caso delle teorie elettromagnetiche di James Clerk Maxwell per illustrare il ruolo dei modelli e dell' analogia nella produzione di nuova conoscenza fisica.
  In particolare, discuteremo di come il modello dei vortici nel suo articolo 'On Physical Lines of Forces' (1861-62) e l'utilizzo del ragionamento analogico abbiano avuto un ruolo centrale nella formulazione delle famose equazioni elettromagnetiche.
  Come evidenziato da diversi studi, descrivere gli aspetti storici ed epistemologici di episodi centrali nella storia della scienza è importante dal punto di vista didattico, dal momento che contribuisce ad una migliore comprensione da parte degli studenti del ruolo chiave dei modelli nella ricerca scientifica e allo sviluppo di competenze modellistiche.
- 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
dic 15 mer 2021

Seminar
Irina Markina, From Clifford algebras to Heisenberg type Lie algebras, 15-12-2021, ore 17:00
- Seminar
- Irina Markina
- University of Bergen, Norway
- From Clifford algebras to Heisenberg type Lie algebras
- Mercoledì 15 dicembre 2021 alle ore 17:00
- On line
- Abstract
  
  As it is well known, the Clifford algebras have numerous applications. In the present talk, we will explain how the Clifford algebras and their representation can build two-step nilpotent Lie algebras. They received the name Heisenberg type Lie algebras, due to the fact that the classical Heisenberg algebra is the simplest example in this construction.
  
  A special class of Heisenberg type Lie algebras was introduced by A. Kaplan in 1980 to study hypoelliptic partial differential operators and their fundamental solutions. The Heisenberg type Lie algebras admit rational structural constants, that lead to the existence of lattices on the corresponding Lie groups according to the Malcev theorem. The factor of Heisenberg type Lie groups by the lattices gives rise to a chain of examples of nilmanifolds that are isospectral but non-diffeomorphic.
  
  In the talk, we will explain the construction of the Heisenberg type Lie algebras and give examples. We also will discuss the classification of the constructed Lie algebras and their group of automorphisms.
- 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
gen 12 mer 2022

Seminar
Andrea Pascucci, Didattica della Probabilità: idee e applicazioni, 12-01-2022, ore 15:00
- Seminar
- Andrea Pascucci
- Università di Bologna
- Didattica della Probabilità: idee e applicazioni
- Mercoledì 12 gennaio 2022 alle ore 15:00
- online tiny.cc/fds22webex
- 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
gen 26 mer 2022

Seminar
Flavia Mammana & Eugenia Taranto, Percorsi di matematica all'aperto con MathCityMap, 26-01-2022, ore 15:00
- Seminar
- Flavia Mammana & Eugenia Taranto
- Università di Catania
- Percorsi di matematica all'aperto con MathCityMap
- Mercoledì 26 gennaio 2022 alle ore 15:00
- online tiny.cc/fds22webex
- 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 09 mer 2022

Seminar
Fabio Zucca, Impariamo a contare: introduzione all'analisi combinatoria, 09-02-2022, ore 15:00
- Seminar
- Fabio Zucca
- Politecnico di Milano
- Impariamo a contare: introduzione all'analisi combinatoria
- Mercoledì 9 febbraio 2022 alle ore 15:00
- online tiny.cc/fds22webex
- 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