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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.

Field of science

  • /natural sciences/computer and information sciences/computational science
  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations
  • /natural sciences/physical sciences/classical mechanics/fluid mechanics/fluid dynamics
  • /natural sciences/mathematics/applied mathematics/mathematical physics
  • /natural sciences/mathematics/pure mathematics/algebra/algebraic geometry
  • /natural sciences/physical sciences/plasma physics

Call for proposal

H2020-MSCA-RISE-2017
See other projects for this call

Funding Scheme

MSCA-RISE - Marie Skłodowska-Curie Research and Innovation Staff Exchange (RISE)

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)

SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE
Italy
EU contribution
€ 184 500
Address
Via Bonomea 265
34136 Trieste
Activity type
Higher or Secondary Education Establishments
UNIVERSITE D'ANGERS
France
EU contribution
€ 99 000
Address
Rue De Rennes 40
49035 Angers Cedex 01
Activity type
Higher or Secondary Education Establishments
COMMUNAUTE D' UNIVERSITES ET ETABLISSEMENTS UNIVERSITE BOURGOGNE - FRANCHE - COMTE
France
EU contribution
€ 162 000
Address
32 Avenue De L'observatoire
25000 Besancon
Activity type
Higher or Secondary Education Establishments

Partners (6)

THE TRUSTEES OF INDIANA UNIVERSITY
United States
Address
Po Box 1847
47402 Bloomington
Activity type
Higher or Secondary Education Establishments
UNIVERSITY OF OTAGO
New Zealand
Address
Saint David Street
9054 Dunedin
Activity type
Higher or Secondary Education Establishments
UNIVERSITE DE MONTREAL
Canada
Address
Cp 6128 Station Centre Ville
H3C3J7 Montreal
Activity type
Higher or Secondary Education Establishments
TSINGHUA UNIVERSITY
China
Address
Qing Hua Yuan
100084 Beijing
Activity type
Higher or Secondary Education Establishments
THE UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
United States
Address
"Airport Drive 104 Suite 2200 Cb #1350"
27599 Chapel Hill
Activity type
Higher or Secondary Education Establishments
BOARD OF GOVERNORS OF THE COLORADO STATE UNIVERSITY SYSTEM
United States
Address
Colorado State University
80523 2001 Fort Collins
Activity type
Higher or Secondary Education Establishments