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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

*11th DFG–CNRS WORKSHOP Micro-Macro Modeling and Simulation of Liquid-Vapor Flows*

*organized with the financial support of*

*DFG, CNRS, and ITN*

**Wednesday March 2nd, 2016** (afternoon)

**Wednesday March 2nd, 2016**(afternoon)

**to ****Friday March 4th, 2016** (at noon)

**to**

**Friday March 4th, 2016**(at noon)

*Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, Paris. **Subway station: Jussieu *

*Lecture room 15-16 — 309*

*Lecture room 15-16 — 309*

*____________________________*

**INVITED SPEAKERS**

**Nina Aguillon** (Paris)

**Nina Aguillon**

**Christophe Berthon** (Nantes)

**Christophe Chalons** (Versailles)

**Frédéric Coquel** (Palaiseau)

**Johannes Daube** (Freiburg)

**Bruno Després** (Paris)

**Christian Dickopp** (Aachen)

**Florence Drui** (Châtenay-Malabry)

**Robert Eymard** ** (**Marne-La-Vallée)

**Jan Giesselman** (Stuttgart)

**Philippe Helluy** (Strasbourg)

**Mirko Kraenkel** (Freiburg)

**Dietmar Kroener** (Freiburg)

**Rüdiger Müller** (Berlin)

**Carlos Pares** (Malaga)

**Arnold Reusken** (Aachen)

#### ____________________________

**Main organizer**

**Philippe G. LeFloch (Paris)**

**Co-organizers**

**Dietmar Kroener (Freiburg)**

**Frédéric Coquel (Palaiseau)**

**SCHEDULE**

__Wednesday afternoon__*(Chairman P.G. LeFloch)*

**Robert Eymard**

**(**Marne-La-Vallée)

**Jan Giesselman**(Stuttgart)

*Coffee break*

**Philippe Helluy**(Strasbourg)

**Mirko Kraenkel**(Freiburg)

__Thursday morning__*(Chairman*

*Jan Giesselman)*

**Christophe Berthon**(Nantes)

**Johannes Daube**(Freiburg)

*Coffee break*

**Christophe Chalons**(Versailles)

**Dietmar Kroener**(Freiburg)

*Lunch break*

**Thursday afternoon***(Chairman F. Coquel)*

**Bruno Després**(Paris)

**Arnold Reusken**(Aachen)

*Coffee break*

**Nina Aguillon**(Paris)

**Rüdiger Müller**(Berlin)

__Friday morning__*(Chairman D. Kroener)*

**Carlos Pares**(Malaga)

**Florence Drui**(Châtenay-Malabry)

**Christian Dickopp**(Aachen)

**Frédéric Coquel**(Palaiseau)

**Nina Aguillon**(Paris)

__Numerical approximation of hyperbolic systems containing an interface__

**Christophe Berthon** (Nantes) __Numerical convergence rate for a diffusive limit of hyperbolic systems: p-system with damping__

**Christophe Chalons**(Versailles)

__On all regime Lagrangian-remap numerical schemes for compressible fluid systems__

*Abstract.*It is the purpose of this contribution to provide an overview on recent advances in the development of all-regime Lagrange-Remap numerical schemes for compressible fluids systems with source terms. We will consider in particular the case of large friction coefficients and the case of low-Mach numbers. More precisely, we will present a discretization strategy for gas dynamics equations for unstructured grids based on a Lagrange-Remap approach that does not involve any moving mesh. A natural semi-implicit extension of the method that allows to remain stable under a CFL condition involving only the material velocity will be given, together with an extremely simple modification that allows to provide an accurate and stable solver for simulations involving low-Mach regions in the flow. The stability properties of the proposed schemes and several numerical experiments will be presented. This contribution is based on a series of joint works with Mathieu Girardin and Samuel Kokh. These works were performed during M. Girardin’s PhD thesis.

**Johannes Daube**(Freiburg)

__Sharp interface limit for the Navier–Stokes–Korteweg model__

*Abstract.* The Navier–Stokes–Korteweg model, an extension of the compressible Navier–Stokes equations, is a diffuse interface model for liquid-vapour flows which allows for phase transitions. In the model, a small parameter represents the thickness of an interfacial area, where phase transitions occur. Its static version was studied by Hermsdoerfer, Kraus and Kroener and the corresponding interface conditions were obtained. Assuming convergence of an associated energy functional to a suitable surface measure, we will perform the sharp interface limit in the dynamic case. More precisely, by means of compactness, we will ensure that solutions to the diffusive Navier-Stokes-Korteweg equations converge to solutions of an appropriate sharp interface model as the interface thickness tends to zero. This is joint work with H. Abels (Regensburg), C. Kraus (Wuerzburg-Schweinfurt) and D. Kroener (Freiburg).

**Bruno Després**(Paris) Modeling uncertainties with kinetic equations

**Christian Dickopp**(Aachen)

__Coupling of (elastic)-plastic solids with compressible two-phase fllows for cavitation damaging__

**Florence Drui**(Châtenay-Malabry)

__A hierachy of homogeneous two-fluid models and numerical methods for simulating various regimes of two-phase flows__

**Robert Eymard (**Marne-La-Vallée)

__Convection and total variation flow__

*Abstract*. We consider a simplified model, related to the flow of a nonNewtonian fluid. This simplified model consists in a scalar nonlinear hyperbolic equation, regularized by the total variation flow operator (or 1-Laplace operator). We give an entropy weak formulation, for which we prove the uniqueness of the solution using the doubling variable technique. We provide an existence result using the convergence of a numerical scheme, a splitting scheme where the hyperbolic flow is treated with finite volumes and the total variation flow with finite elements. Finally, some numerical simulations in 1D and 2D are presented. This work is a joint work with F. Bouchut and D. Doyen.

**Jan Giesselman**(Stuttgart)

__A priori error analysis of DG approximations of two-phase flows__

*Abstract.* In this talk we consider a one dimensional model for isothermal two-phase flows using Lagrangian coordinates. The model is of diffuse interface type with a non-monotone pressure law. We will present a priori error analysis of a semi-discrete discontinuous Galerkin method, which satisfies a discrete version of the energy inequality which is valid on the continuous level. It also satisfies a relative energy type stability theory. Combining this stability framework with suitable projection operators for the exact solution allows us to derive optimal order error estimates. We will also present numerical results obtained using a fully-discrete version of the scheme, which validate our theoretical results.

**Philippe Helluy**(Strasbourg)

__Task-based parallelization of a transport discontinuous Galerkin solver and applications.__

**Mirko Kraenkel**(Freiburg)

__Discontinuous Galerkin schemes for the Navier-Stokes-Allen-Cahn system__

**Dietmar Kroener**(Freiburg) Conservation laws on surfaces

**Rüdiger Müller**(Berlin)

__The Lippmann equation for liquid metal electrodes__

**Carlos Pares**(Malaga)

__Nonconservative products and Shallow Water models: an overview__

*Abstract.*Many hyperbolic nonlinear PDE systems that include source terms and nonconservative products arise in the simulation of geophysical flows by means of depth-averaged models. In this talk, a review of the numerical techniques developed in last years by my group of research and collaborators to solve this type of systems will be presented together with a discussion of the main difficulties and challenges in this field. Some applications to the simulation of real flows will be shown to illustrate this topic.

**Arnold Reusken**(Aachen)

__Space-time unfitted FEM for problems with moving discontinuities__

*Abstract.*In this talk we will discuss unfitted finite element methods (or CutFEM) in a space-time setting. The motivation for the development of these methods comes from two-phase incompressible flows. We explain how these techniques can be applied for the accurate discretization of a mass transport equation and a two-phase flow (Navier-)Stokes equation. The idea of the method, rigorous error bounds for certain problem classes and results of numerical experiments will be presented.

**Partial LIST of Participants**

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**PRACTICAL INFORMATIONS **

How to come to the Laboratoire Jacques-Louis Lions

Hotels near the University Pierre et Marie Curie

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**EARLIER WORKSHOPS “Micro-Macro Modeling and Simulation of Liquid-Vapor Flows”**

Tenth Workshop, Freiburg, February 2015

Ninth Workshop, Paris, February 2014

Eight Workshop, Berlin, February 2013

Seventh Workshop, Paris, February 2012

Sixth Workshop, Stuttgart, January 2011

Fifth Workshop, Strasbourg, April 2010

Fourth Workshop, Aachen, February 2009

Third Workshop, Strasbourg, January 2008

Second Workshop, Bordeaux, November 2007

Opening Workshop, Kirchzarten, November 2005

**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- 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.