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Workshop 2016
“Modeling and Computation of Shocks and Interfaces”
Laboratoire Jacques-Louis Lions
Université Pierre et Marie Curie, Paris
Organizers
Philippe G. LeFloch (Paris)
Charalambos Makridakis (Brighton)
Supported by the ModCompShock ITN project
and a project PICS CNRS
Dec. 6 around 1:30pm to Dec. 8 around 1pm
Main speakers
Remi Abgrall (Zurich)
Benjamin Boutin (Rennes)
Christophe Chalons (Versailles)
Sergey Gavrilyuk (Marseille)
Charalambos Makridakis (Brighton)
Pierangelo Marcati (L’Aquila)
Siddhartha Mishra (Zurich)
Carlos Pares (Malaga)
Nils Risebro (Oslo)
Giovanni Russo (Catania)
Lev Truskinovsky (Palaiseau)
Titles of the lectures
Benjamin Boutin Numerical boundary layers for linear hyperbolic IBVP and semigroup estimate
Christophe Chalons On the computation of non conservative products and cell averages in finite volume methods
Makridakis Charalambos Energy/entropy consistent computational methods
Sergey Gavrilyuk Shock-droplet interaction via a new hyperbolic phase field model
Pierangelo Marcati Splash singularities for incompressible viscoelatic fluids
Siddhartha Mishra Statistical solutions of systems of conservation laws
Carlos Pares Entropy stable schemes for degenerate convection-diffusion equations
Nils Risebro Numerical methods for scalar conservation laws with a stochastically driven flux
Giovanni Russo Shock capturing schemes for all Mach number flow in gas dynamics
Lev Truskinovsky Solitary waves in the FPU lattice: from quasi-continuum to anti-continuum limit
Schedule of the workshop
Tuesday afternoon
2pm-2:45pm: C. Makridakis
2:45-3:30pm: C. Pares
3:30pm: coffee break
4pm-4:45pm G. Russo
Wednesday morning
10am-10:45am: S. Gavrilyuk
10:45am: coffee break
11:15am: C. Chalons
Noon: lunch buffet
Wednesday afternoon
2pm-2:45pm R. Abgrall
2:45pm-3:30pm S. Mishra
3:30am coffee break
4pm L. Truskinovsky
Thursday morning
9:30am-10:15am N. Risebro
10:15am coffee break
10:45am B. Boutin
11:30am P. Marcati
12:15 lunch buffet (end of the workshop)
Participants to the workshop
- Remi Abgrall (Zurich) remi.abgrall at math.uzh.ch
- Benjamin Boutin (Rennes) chalons at math.jussieu.fr
- Christophe Chalons (Versailles) chalons at math.jussieu.fr
- Yangyang Cao (Paris) caoyangyang0721 at 163.com
- Marco De Lorenzo (Paris) marco.de-lorenzo at edf.fr
- Christian Dickopp (Aachen) dickopp at web.de
- Alain Forestier (Saclay) alain.forestier at cea.fr
- Sergey Gavrilyuk (Marseille) sergey.gavrilyuk at univ-amu.fr
- Maren Hantke (Magdeburg) maren.hantke at ovgu.de
- David Iampetro (Marseille) david.iampietro at edf.fr
- Philippe G. LeFloch (Paris) contact philippelefloch.org
- Charalambos Makridakis (Brighton) C.Makridakis at sussex.ac.uk
- Pierangelo Marcati (L’Aquila) pierangelo.marcati at gssi.infn.it
- Christoph Matern (Magdeburg) christoph.matern at ovgu.de
- Siddhartha Mishra (Zurich) siddhartha.mishra at sam.math.ethz.ch
- Roberto Molina (Paris) rmolina.sep at gmail.com
- Hieu Nguyen (Aachen) nguyen at instmath.rwth-aachen.de
- Carlos Pares (Malaga) pares at anamat.cie.uma.es
- Yohan Penel (Paris) penel at ann.jussieu.fr
- Chaoyu Quan (Paris) quanchaoyu at gmail.com
- Pierre-Arnaud Raviart (Paris) pa at raviart.com
- Nils Risebro (Oslo) nilshr at math.uio.no
- Giovanni Russo (Catania) russo at dmi.unict.it
- Lev Truskinovsky (Palaiseau) trusk at lms.polytechnique.fr
- Shugo Yasuda (Hyogo) yasuda at sim.u-hyogo.ac.jp
- Dimitrios Zacharenakis (Stuttgart) zachards at mathematik.uni-stuttgart.de
Other practical informations
The workshop will take place in the main lecture room 309 of the Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, which is located in the building 15-16.
Address: 4 Place Jussieu, 75258 Paris. Subway station: Jussieu.
List of hotels in the vicinity of the university
September 14, 2015 to December 18, 2015
Trimester Program at the
Centre Emile Borel
Financial support provided by Institut Henri Poincaré
and ANR Project “Mathematical General Relativity”
Organizers
Lars Andersson (Potsdam)
Sergiu Klainerman (Princeton)
Philippe G. LeFloch (Paris)
MAIN THEMES OF THE PROGRAM
Einstein’s field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts (Cauchy problem, cosmic censorship, asymptotic behavior). These developments have brought into focus the deep connections between the Einstein equation and other important geometric PDE’s, including the wave map equation, Yang-Mills equation, Yamabe problem, as well as Hamilton’s Ricci flow. The field is of growing interest for mathematicians and of intense current activity, as is illustrated by major recent breakthrough, concerning the uniqueness and stability of the Kerr black hole model, the formation of trapped surfaces, and the bounded L2 curvature problem. Specifically, the themes of mathematical interest that will be developed in the present Program and are currently most active include:
- The initial value problem for Einstein equation and the causal geometry of spacetimes with low regularity, formation of trapped surfaces
- Techniques of Lorentzian geometry: injectivity radius estimates, geometry of null cones; construction of parametrix
- Geometry of black hole spacetimes: uniqueness theorems, censorship principles
- Coupling of Einstein equation for self-gravitating matter models, weakly regular spacetimes, nonlinear stability of Minkowski space with matter
General schedule for the Trimester
SCIENTIFIC ACTIVITIES during the Trimester
- Workshops and Conferences (see below)
- On the Mathematical Theory of Black Holes, Course by S. Klainerman.
- Begins on October 13 from 2pm to 4:30pm, and the following Tuesdays.
- Video of the lectures
- An Introduction to Self-Gravitating Matter, Course by P.G. LeFloch.
- Begins on October 9 from 2pm to 4:30pm, and the following Fridays.
- LECTURE NOTES for this course
- Video 1: An introduction to self-gravitating matter
- Video 2: Modified gravity and weakly regular spacetimes
- Video 3: Weak solutions to the Einstein equations
- Video 4: Weakly regular Cauchy developments
- Video 5: Self-gravitating fluids with bounded variation
- Video 6: The geometry of weakly regular spacetimes
- Video 7: Nonlinear stability of Minkowski space for massive fields
- Weekly Seminar on Mathematical General Relativity
- organized by L. Andersson, jointly with S. Klainerman, P.G. LeFloch, J. Szeftel (Paris), and A. Zeghib (Lyon).
- Begins on October 7 from 2pm to 4:30pm, and the following Wednesdays.
- Speakers in the Seminar :
- Bruno Premoselli (Cergy-Pontoise), Martin Taylor (Cambridge, UK)
- Steffen Aksteiner (Potsdam), Lars Andersson (Potsdam)
- Jesus Oliver (San Diego)
- Anne Franzen (Utrecht), Jared Wunsch (Evanston)
- Sung-Jin Oh (Berkeley), Anna Sakovich (Vienna)
- Hans Lindblad (Baltimore), Florian Beyer (Dunedin)
- VIDEOS available (courses, main conference)
- Tea break every day 3pm-3:30pm
WORKSHOPS AND CONFERENCES
Sept. 14 to 18, 2015 Summer School – INTRODUCTION TO MATHEMATICAL GENERAL RELATIVITY
List of speakers
Greg Galloway (Miami)
Gerhard Huisken (Tuebingen)
Hans Ringstrom (Stockholm)
Sept. 23 to 25, 2015 Workshop – RECENT ADVANCES IN MATHEMATICAL GENERAL RELATIVITY
List of speakers
Spyros Alexakis (Toronto)
Piotr Chrusciel (Vienna)
Joao Costa (Lisbon)
Semyon Dyatlov (Cambridge, USA)
Stefan Hollands (Cardiff)
Alexandru Ionescu (Princeton)
Lionel Mason (Oxford)
Vincent Moncrief (Yale)
Jean-Philippe Nicolas (Brest)
Harvey Reall (Cambridge, UK)
Hans Ringstrom (Stockholm)
Mu-Tao Wang (New York)
Sept. 28 to Oct. 1, 2015 Workshop – GEOMETRIC ASPECTS OF MATHEMATICAL RELATIVITY (Hold in Montpellier and organized by Marc Herzlich and Erwann Delay)
List of speakers
Piotr Chrusciel (Vienna)
Michael Eichmair (Zürich)
Mu-Tao Wang (New York)
Oct. 26 to 29, 2015 Workshop – DYNAMICS OF SELF-GRAVITATING MATTER
List of speakers
Hakan Andreasson (Gothenburg)
Thierry Barbot (Avignon)
Robert Beig (Vienna)
David Fajman (Vienna)
Marc Mars (Salamanca)
David Maxwell (Fairbanks)
Todd Oliynyk (Monash)
Volker Schlue (Toronto)
Bernd Schmidt (Potsdam)
Jared Speck (Cambridge, USA)
Shadi Tahvildar-Zadeh (Rutgers)
Eric Woolgar (Alberta)
Nov. 16 to 20, 2015 International Conference – GENERAL RELATIVITY – A Celebration of the 100th Anniversary
List of speakers Schedule and title
Jean-Pierre Bourguignon (Bures-sur-Yvette)
Demetrios Christodoulou (Zürich & Athens)
Mihalis Dafermos (Princeton)
Thibault Damour (Bures-sur-Yvette)
Georges Ellis (Cape Town)
Richard Hamilton (New York)
Gustav Holzegel (London)
Jonathan Luk (Cambridge, UK)
Roger Penrose (Oxford)
Richard Schoen (Stanford & Irvine)
Jacques Smulevici (Orsay)
Jérémie Szeftel (Paris)
Robert Wald (Chicago)
Qian Wang (Oxford)
Dec. 14 to 16, 2015 International Conference- RELATIVITY AND GEOMETRY – IN MEMORY OF A. LICHNEROWICZ (Organized by Giuseppe Dito, Jean-Pierre Francoise, Paul Gauduchon, Richard Kerner, Yvette Kosmann-Schwarzbach et Daniel Sternheimer)
List of speakers
Olivier Biquard (Paris 6)
Robert Bryant (Durham)
Pierre Cartier (Gif-Sur-Yvette)
Thibault Damour (Gif-Sur-Yvette)
Nathalie Deruelle (Paris 7)
Simon Donaldson (Stony Brook & London)
Michel Dubois-Violette (Paris 11)
Charles Francès (Strasbourg)
Edward Frenkel (Berkeley)
Christian Fronsdal (Los Angeles)
Simone Gutt (Bruxelles)
James Isenberg (Eugene)
Sergiu Klainerman (Princeton)
Maxim Kontsevich (Gif-Sur-Yvette)
Alan Weinstein (Berkeley)
Program coordinated by the Centre Emile Borel at IHP. Financial support provided by the Institut Henri Poincaré and the ANR Project “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”.
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Organizers
Michael Anderson (Stony Brook)
Sergiu Klainerman (Princeton)
Philippe G. LeFloch (Paris)
Jared Speck (Cambridge, USA)
Location: Simons Center for Geometry and Physics
Date: One-month concentration period in January 2015
Workshop from January 20 to 23, 2015
Einstein’s field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts, including the Cauchy problem, cosmic censorship, and asymptotic behavior. These developments have brought into focus the deep connections between the Einstein equation and other important geometric partial differential equations, including the wave map equation, Yang-Mills equation, Yamabe equation, as well as Hamilton’s Ricci flow. The field is of growing interest for mathematicians and of intense current activity, as is illustrated by major recent breakthroughs concerning the uniqueness and stability of black hole models, the formation of trapped surfaces, and the bounded L2 curvature problem. The themes of mathematical interest that will be particularly developed in the present Program include the formation of trapped surfaces and the nonlinear interaction of gravitational waves. The new results are based on a vast extension of the earlier technique by Christodoulou and Klainerman establishing the nonlinear stability of the Minkowski space. This Program will be an excellent place in order to present the recent breakthrough on the bounded L2 curvature problem for the Einstein equation, which currently provides the lower regularity theory for the initial value problem, as well as the recently developed theory of weakly regular Einstein spacetimes with distributional curvature.
Long-term participants
Michael Anderson (Stony Brook)
Piotr Chrusciel (Vienna)
Mihalis Dafermos (Princeton)
Cécile Huneau (Paris)
Alexandru D. Ionescu (Princeton)
James Isenberg (Eugene)
Sergiu Klainerman (Princeton)
Philippe G. LeFloch (Paris)
Jared Speck (Cambridge, USA)
Jinhua Wang (Hangzhou)
Mu-Tao Wang (New York)
Qian Wang (Oxford)
Willie Wong (Lausanne)
Speakers during the Workshop
- Tuesday January 20
- Sung-Ji Oh (Berkeley) Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations
- Volker Schlue (Toronto) Stationarity of time-periodic vacuum spacetimes
- Alexandru D. Ionescu (Princeton) The Euler–Maxwell system for electrons: global solutions in 2D
- Joachim Krieger (Lausanne) Concentration-compactness for the critical Maxwell-Klein-Gordon equation
- Wednesday January 21
- Xianliang An (Piscataway) Two results on formation of trapped surfaces
- Tahvildar-Zadeh (Piscataway) The Dirac electron and the Kerr-Newman spacetime
- Mihalis Dafermos (Princeton)
- Jim Isenberg (Eugene) Asymptotically hyperbolic shear-free solutions of the Einstein constraint equations
- Thursday January 22
- Cécile Huneau (Paris) Stability in exponential time of Minkowski
- Jacques Smulevici (Orsay) Vector field methods for transport equations with applications to the Vlasov-Poisson system
- Mu-Tao Wang (New York) Quasi-local angular momentum and the limit at infinity
- Spyros Alexakis (Toronto) The Penrose inequality for perturbations of the Schwarzschild exterior
- Friday January 23
- Mihai Tohaneanu (Statesboro) Pointwise decay for the Maxwell system on black holes
- Qian Wang (Oxford)
- Peter Blue (Edinburgh) Revisiting decay of fields outside a Schwarzschild black hole
- Philippe G. LeFloch (Paris) Weak solutions to the Einstein equations in spherical or T2 symmetry
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Organizers
Philippe G. LeFloch (Paris)
Jérémie Szeftel (Paris)
Ghani Zeghib (Lyon)
ANR Project
“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”
Wednesday June 17, 2015
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris
Lecture room 15/25-326
11h Emmanuel Hebey (Cergy-Pontoise) Systèmes de Kirchhoff critiques stationnaires sur des variétés compactes
14h Lydia Bieri (Ann Arbor) Gravitational radiation and two types of memory
Abstract. We are believed to live on the verge of detection of gravitational waves, which are predicted by General Relativity. In order to understand gravitational radiation, we have to investigate analytic and geometric properties of corresponding solutions to the Einstein equations. Gravitational waves leave a footprint in the spacetime regions they pass, changing the manifold – and therefore displacing test masses – permanently. This is known as the memory effect. It has been believed that for the Einstein equations, being nonlinear, there exists one such effect with a small `linear’ and a large `nonlinear’ part. In this talk, I present some of my joint work with D. Garfinkle showing that these are in fact two different effects.
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Organizers
Philippe G. LeFloch (Paris)
Jérémie Szeftel (Paris)
Ghani Zeghib (Lyon)
ANR Project
“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”
Wednesday May 27, 2015
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris
Lecture room 15-25–326
14h Thierry Barbot (Avignon) Surfaces polygonales fuchsiennes et espace de Teichmüller décoré
Abstract. Dans l’article “Fuchsian polyhedra in Lorentzian space-forms, Mathematische Annalen 350, 2, pp. 417-453, 2011″, F. Fillastre a montré que toute métrique euclidienne avec singularités coniques d’angles > 2 pi sur une surface compacte se réalise de manière unique comme une surface de Cauchy polygonale dans un espace-temps globalement hyperbolique localement plat radial (i.e. dont le groupe d’holonomie fixe un point de l’espace de Minkowski). Dans cet exposé, j’évoquerai le travail de L. Brunswic dans son travail de thèse sous ma direction, qui vise à reprouver ce résultat et à l’étendre au cas des surfaces polygonales dans un espace-temps localement plat mais admettant des particules massives. Le but est de montrer qu’il y a encore existence et unicité une fois prescrit la masse des particules massives (le cas régulier montré par Fillastre correspondant au cas où l’angle singulier des particules massives est 2pi). Je montrerai aussi que la situation étudiée par R. Penner dans l’article “The Decorated Teichmϋller Space of Punctured Surfaces, Commun. Math. Phys. 113, 299-339 (1987)” est un cas limite de la situation étudiée par Brunswic, et correspond au cas où les particules sont d’angle conique nul. Je montrerai aussi comment répondre positivement à la question dans le cas où il n’y a qu’une singularité.
15h30 Andrea Seppi (Pavia) Convex surfaces in (2+1)-dimensional Minkowski space
Abstract. It is known that the hyperbolic plane admits an isometric embedding into Minkowski space; in 1983 Hanu and Nomizu first observed the existence of non-equivalent isometric embeddings, thus showing a relevant difference with the Euclidean case. In this talk, I will introduce some natural properties of a convex surface in Minkowski space, concerning causality and asymptotic behavior. I will then explain some new results (jointly with Francesco Bonsante) on the classification of constant curvature surfaces with bounded principal curvatures and on the solvability of Minkowski problem in (2+1)-dimensional Minkowski space. If time permits, I will give the main ideas of the proof and especially the relation to some type of Monge-Ampere equations.
