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Integrable Partial Differential Equations: Geometry, Asymptotics, and Numerics.

Integrable Partial Differential Equations: Geometry, Asymptotics, and Numerics.

Objective

Partial Differential Equations (PDE's) undoubtedly are among the main tools for an efficient modelling of physical phenomena. Infinite-dimensional analogues of regular (integrable) behaviour, previously confined to the theory of systems with a finite number of degrees of freedom began to be considered in the middle of the XX century in fluid dynamics, field theory and plasma physics.
The idea that an integrable behaviour persists in non-integrable systems, together with the combination of the state-of-the-art numerical methods with front-line geometrical and analytical techniques in the theory of Hamiltonian PDE's is the leitmotiv of this research project.
Asymptotic regimes leading to phase transitions both in the theory of dispersive PDEs and the theory of Random Matrices display universality properties which can be analysed both numerically and analytically. The predictive power of numerics and scientific computing can be used both as a testing tool for theoretical models and as a generator of new conjectures.
By focussing the expertise of front line researchers in different areas of Mathematics towards the study of critical phenomena in dispersive PDE's, we expect results in realms including differential and algebraic geometry, the theory of random matrices, multiscale analysis of PDE's as well as non-linear models of stratified fluid flows.
The broad interdisciplinary basis and intertwining of methods of Geometry and Mathematical Physics will be instrumental in making the results accessible for the wider community. Younger (Ph.D. and/or Post-Docs) Researchers to be included in such an active and fertile research and training ground, will certainly seize their chance to enhance and broaden their skills.
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Coordinator

UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA

Address

Piazza Dell'Ateneo Nuovo 1
20126 Milano

Italy

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 94 500

Participants (3)

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SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE

Italy

EU Contribution

€ 184 500

UNIVERSITE D'ANGERS

France

EU Contribution

€ 99 000

COMMUNAUTE D' UNIVERSITES ET ETABLISSEMENTS UNIVERSITE BOURGOGNE - FRANCHE - COMTE

France

EU Contribution

€ 162 000

Partners (6)

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THE TRUSTEES OF INDIANA UNIVERSITY

UNIVERSITY OF OTAGO

UNIVERSITE DE MONTREAL

TSINGHUA UNIVERSITY

THE UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL

BOARD OF GOVERNORS OF THE COLORADO STATE UNIVERSITY SYSTEM

Project information

Grant agreement ID: 778010

Status

Ongoing project

  • Start date

    1 January 2018

  • End date

    31 December 2021

Funded under:

H2020-EU.1.3.3.

  • Overall budget:

    € 886 500

  • EU contribution

    € 540 000

Coordinated by:

UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA

Italy