You are currently browsing the category archive for the ‘ALL SEMINARS AND CONFERENCES’ category.

###### _____________________________**_______________****_________________________________________****_______________**_________

**_________________________________________**

#### Seminar at the

#### Laboratoire Jacques-Louis Lions

#### Université Pierre et Marie Curie, Paris

*Organizers*

#### Philippe G. LeFloch (Paris)

#### Jacques Smulevici (Orsay)

#### Jérémie Szeftel (Paris)

**Dates of the Seminar: **

**January 30, February 27, March 20, April 10, May 22, June 6, June 19, July 4**

#### Monday January 30, 2017

*room 15/25-104*

#### 14h Georgios Moschidis (Princeton, USA)

**The scalar wave equation on general asymptotically flat spacetimes. Stability and instability results**

Abstract. We will examine how certain geometric conditions on general asymptotically flat spacetimes (M,g) are related to stability or instability properties of solutions to the scalar wave equation on M. First, in the case when (M,g) possesses an event horizon with positive surface gravity and an ergo-region which is sufficiently small in terms of the near-horizon geometry, we will prove a logarithmic decay result for solutions to the wave equation, provided a uniform energy boundedness estimate holds. This result, applicable also in the absence of a horizon and an ergo-region, generalizes a result of Burq for the wave equation on the complement of an arbitrary compact obstacle in flat space. We will then apply the methods developed for the proof of this result in obtaining a rigorous proof of Friedman’s ergosphere instability for scalar waves in the case when (M,g) possesses an ergo-region and no event horizon.

#### 15h30 Xavier Lachaume (Tours)

**The constraint equations of scalar tensor and Lovelock theories**

Abstract. The ADM decomposition is the projection of the Einstein field equations on a spacelike foliation of the spacetime. It gives the constraint equations that must necessarily be satisfied by a riemannian metric and a 2-form to be the initial data of an Einstein spacetime. In this talk, we shall introduce some modified gravity theories: the scalar-tensor and Lovelock theories, and see how they behave under the ADM decomposition. We shall examine their constraint equations, and solve them in particular cases. This involves the study of whether a certain function of the elementary symmetric polynomials is concave or not.

#### Monday February 27, 2017

*room 15/16-309*

#### 14h Mokdad Mokdad (Brest)

**Conformal scattering for Maxwell fields on Reissner-Nordstrøm-de Sitter spacetimes**

Abstract. The Reissner-Nordstrøm-de Sitter spacetime models a spherically symmetric charged and non-rotating black hole in the presence of a positive cosmological constant. Depending on the parameters of the metric, this spacetime can have up tothree distinct event horizons. In the case of three horizons, we develop a scattering theory for Maxwell fields using the conformal geometric approach initiated by Penrose and Friedlander and referred to as conformal scattering. The idea is that a complete scattering theory is equivalent to the well-posedness of the Goursat problem (characteristic Cauchy problem) at the null boundary of the conformal manifold. Decay estimates obtained by geometric energy inequalities are essential tools for closing the estimates that allow the construction of the scattering operator : their role is to prove that energy cannot accumulate at timelike infinity, which can be understood as a weak form of Huygens’ principle.

#### 15h30 Annalaura Stingo (Paris 13)

**Global existence and asymptotic behavior for small solutions to 1D quasi-linear cubic Klein-Gordon equations**

Abstract. Let u be a solution to a quasi-linear cubic Klein-Gordon equation, with smooth, small Cauchy data. It is known that, under a suitable condition on the nonlinearity, the solution is global-in-time for compactly supported Cauchy data. We prove that the result holds even when data are not compactly supported but only decay like 1/r at infinity, combining the method of Klainerman vector fields with a semiclassical normal forms method introduced by Delort. Moreover, we get a one-term asymptotic expansion for the solutions and establish a modified scattering property.

#### Monday March 20, 2017

*room 15/16-309*

#### 14h Dominic Dold (Cambridge, UK)

**Exponentially growing mode solutions to the Klein-Gordon equation in Kerr-AdS spacetimes**

Abstract. We consider solutions to the Klein-Gordon equation in the black hole exterior of Kerr-AdS spacetimes. It is known that, if the spacetime parameters satisfy the Hawking-Reall bound, solutions (with Dirichlet boundary conditions at infinity) decay logarithmically. We shall present our recent result of the existence of exponentially growing mode solutions in the parameter range where the Hawking-Reall bound is violated. We will discuss various boundary conditions at infinity.

#### Monday April 10, 2017

*room 15/25-101*

#### 14h Bruno Premoselli (Bruxelles)

**Instability of focusing initial data sets in high dimensions**

Abstract. We will investigate blow-up properties for a class of initial data sets for the Einstein equations obtained from the conformal method in a scalar-field theory. In dimensions larger than 6, and when some stability conditions on the physics data are not satisfied, we will show that the conformal method produces blowing-up families of initial data sets. The proof of this result combines constructive variational methods with a priori asymptotic analysis blow-up techniques.

#### Monday May 22, 2017

*exceptionally taking place at IHES*

*and co-organized with S. Klainerman (Princeton)*

#### 14h Jan Sbierski (Cambridge, UK)

**The inextendibility of the Schwarzschild spacetime as a Lorentzian manifold with a continuous metric**

Abstract. The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this talk I will describe how one proves the stronger statement that the maximal analytic Schwarzschild spacetime is inextendible as a Lorentzian manifold with a continuous metric. The investigation of low-regularity inextendibility criteria is motivated by the strong cosmic censorship conjecture in general relativity.

#### 15h30 Grigorios Fournodavlos (Cambridge, UK)

**Dynamics of the Einstein equations near a Schwarzschild singularity**

Abstract. We will discuss dynamical properties of the Schwarzschild interior, backwards and forwards (in time) with respect to the initial value problem for the Einstein vacuum equations.

#### Tuesday June 6, 2017

*room 15/16-309*

#### 14h Dejan Gajic (London)

**Precise asymptotics for the wave equation on stationary, asymptotically flat spacetimes**

Abstract. The late-time behaviour of solutions to the wave equation on a large class of asymptotically flat spacetimes does not conform to the strong Huygens principle. Instead, it is governed by polynomially decaying “tails”, as first discovered heuristically by Price. Their presence plays an important role in the study of singularities in black hole interiors. I will discuss a method for proving the precise leading-order asymptotics for the wave equation on these spacetimes and in the process I will introduce new energy decay estimates to obtain sharp decay rates that go beyond those obtained via traditional vector field methods. This talk is based on joint work with Yannis Angelopoulos and Stefanos Aretakis.

#### 15h30 Cécile Huneau (Grenoble)

**High frequency back reaction for the Einstein equations under polarized U(1) symmetry**

Abstract. It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency yield at the limit to a non trivial contribution which corresponds to the presence of an energy impulsion tensor in the equation for the background metric. This non trivial contribution is of due to the nonlinearities in Einstein equations, which involve products of derivatives of the metric. It has been conjectured by Burnett that the only tensors which can be obtained this way are massless Vlasov, and it has been proved by Green and Wald that the limit tensor must be traceless and satisfy the dominant energy condition. The known exemples of this phenomena are constructed under symmetry reductions which involve two Killing fields and lead to an energy impulsion tensor which consists in at most two dust propagating in null directions. In this talk, I will explain our construction, under a symmetry reduction involving one Killing field, which lead to an energy impulsion tensor consisting in N dust fields propagating in arbitrary null directions. This is a joint work with Jonathan Luk (Stanford).

#### Monday June 19, 2017

*room 15/16-309*

#### 14h Elena Giorgi (Columbia)

**On the rigidity problem of black holes in general relativity**

Abstract. The rigidity problem in General Relativity consists in showing that an (electro)vacuum, asymptotically flat and stationary spacetime is isometric to Kerr(-Newman). The problem was solved for analytic manifolds by Hawking in the so called “no-hair theorem”. We overview the known results related to the rigidity problem for Ricci flat smooth manifolds. In the non-analytic case, Ionescu-Klainerman extended the Hawking Killing field along the horizon to the outer domain of dependence. This was done through a unique continuation procedure, relying on Carleman estimates. We generalize the result to the case of Einstein equation coupled with Maxwell equations. Finally, we summarize what is known in the case of degenerate horizons, which corresponds to the extremal Kerr.

#### Monday July 3, 2017

*exceptionally taking place at IHES*

*and co-organized with S. Klainerman (Princeton)*

#### 14h Steffen Aksteiner (Potsdam)

**From operator identities to symmetry operators**

Abstract. The hidden symmetry of the Kerr spacetime, encoded in its pair of conformal Killing-Yano tensors, implies hidden symmetries for various test fields on such a background. Starting from certain natural operator identities we derive two such symmetries of the linearized Einstein operator. The first one is of differential order four and the relation to the classical theory of Debye potentials as well as to the Chandrasekhar transformation will be explained. The second one is of differential order six and related to the separability of an integrability condition to the linearized Einstein equations — the Teukolsky equation. Advanced symbolic computer algebra tools for xAct were developed for this purpose and if time permits, I will give an overview on the current status.

#### 15h30 Arick Shao (London)

**Unique continuation of waves on asymptotically Anti-de Sitter spacetimes**

Abstract. In theoretical physics, it is often conjectured that a correspondence exists between the gravitational dynamics of asymptotically Anti-de Sitter (AdS) spacetimes and a conformal field theory of their boundaries. In the context of classical relativity, one can attempt to rigorously formulate such a correspondence statement as a unique continuation problem for PDEs: Is an asymptotically AdS solution of the Einstein equations uniquely determined by its data on its conformal boundary at infinity? In this presentation, we establish a key step: we prove such a unique continuation result for wave equations on fixed asymptotically AdS spacetimes. In particular, we highlight the analytic and geometric features of AdS spacetime which enable this uniqueness result, as well as obstacles preventing such a result from holding in other cases. If time permits, we will also discuss some applications of this result toward symmetry extension and rigidity theorems.

###### _____________________________**_______________****_________________________________________****_______________**_________

**_________________________________________**

#### Seminar at the

#### Laboratoire Jacques-Louis Lions

#### Université Pierre et Marie Curie, Paris

*Organizers*

#### Philippe G. LeFloch (Paris)

#### Jacques Smulevici (Orsay)

#### Jérémie Szeftel (Paris)

This Fall: **October 10, November 21, and December 12, 2016**

#### Monday October 10, 2016

*room 15/25-104*

#### 14h Peter Hintz (Berkeley)

**Nonlinear stability of Kerr-de Sitter black holes**

**Abstract. **In joint work with András Vasy, we recently established the stability of the Kerr-de Sitter family of black holes as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta but without any symmetry assumptions on the initial data. I will explain the general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein’s equations, and thus how our solution scheme finds a suitable (wave map type) gauge within a carefully chosen finite-dimensional family of gauges; I will also address the issue of finding the mass and the angular momentum of the final black hole.

#### 15h30 Stefan Czimek (Paris)

**An extension procedure for the constraint equations**

**Abstract. **In this talk we present a new extension procedure for the maximal constraint equations of general relativity, motivated by applications to the Cauchy problem. Given a small solution on the unit ball, we can extend it to an asymptotically flat global solution. The main features are that our extension procedure does not need a gluing region, preserves regularity and works in weak regularity. For the proof, we use new methods to solve the prescribed divergence equation for the second fundamental form and the prescribed scalar curvature equation for the metric. We use the under-determinedness of the constraint equations to conserve regularity.

#### Monday November 21, 2016

*room 15/16-413*

#### 14h The-Cang Nguyen (Paris)

**Progress and recent results for the conformal equations**

**Abstract. **The presentation will be divided into two parts. First, I will introduce the conformal equations and present recent results for these equations as well as questions arising naturally. In a second part, I will talk about the “half-continuity method” and explain how to use this method for giving answers to the questions posed in the first part.

#### 15h30 Volker Schlue (Paris)

**On the nonlinear stability of expanding black hole cosmologies**

#### Monday December 12, 2016

*room 15/25-102*

#### 14h Michał Wrochna (Grenoble)

**The quantum stress-energy tensor and its intricate relationship with spacetime geometry**

**Abstract. **It is widely believed that at low energies, quantum gravity should yield an effective theory described by Einstein equations with a stress-energy tensor made of averaged fluctuations of quantum fields. The construction of that stress-energy tensor is however very problematic and its intricate dependence on spacetime geometry results in highly non-linear equations that possess no qualitative theory to date. In this talk I will review this problem as a motivation for improving the construction of linear Klein-Gordon quantum fields, and discuss recent progress that allows for a better control of the dependence on the spacetime metric (partly based on joint work with Christian Gérard).

#### 15h30 Guillaume Idelon-Riton (Regensburg)

**Some results about the scattering theory for the massive Dirac fields in the Schwarzschild-Anti-de Sitter space-time**

**Abstract. **I will first give a brief presentation of the Schwarzschild-Anti-de Sitter spacetime and of some of its geometrical properties that will concern us. Then I will present the massive Dirac equation in this space-time and first study the Cauchy problem which is not completely obvious since our spacetime is not globally hyperbolic. I will then give a result concerning the asymptotic completeness for these fields. By means of a Mourre estimate, it is possible to obtain that the minimal velocity for these fields is 1. I will then show that our dynamics behaves in asymptotic regions like a transport at unit speed in the direction of the black hole. In a third part, I will study the local energy decay for these fields. First, using the existence of exponentially accurate quasi-modes, I will show a logarithmic lower bound on the local energy decay which is in accordance with the results of G. Holzegel and J. Smulevici in the Kerr-Anti-de Sitter spacetime for the Klein-Gordon fields. In order to obtain an upper bound, I will prove the existence of resonances and give some tools in order to localize them.

###### _____________________________**_______________****_________________________________________****_______________**_________

**_________________________________________**

#### 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**

#### ____________________________

**PRACTICAL INFORMATIONS **

How to come to the Laboratoire Jacques-Louis Lions

Hotels near the University Pierre et Marie Curie

#### ____________________________

**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”.*