NEWSLETTER - 2011

Léon Motchane, the founderof IHÉS, was a visionary. Increating the Institute, hewanted to give researchers

from all over the world a place of freedom and communication.Keen to offer IHÉS scientists a suitable site for research, hemade it possible for the Institute to acquire the Bois-Marieestate in 1962. Today, the campus is an integral part of the

editorial

table of contentsevents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 - 3professors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5publication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7the Schlumberger Chair . . . . . . . . . . . . . . . . . . . . . 7 - 10the 50th Anniversary Campaign . . . . . . . . . . . . . . . 11 - 15point of view by ... / 2011 events . . . . . . . . . . . . . . . . . 16

Institut des Hautes Études Scientifiques | Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette, FranceTéléphone : +33 1 60 92 66 00 | Télécopie : +33 1 60 92 66 69 | Courrier électronique : comdev@ihes.fr | Site internet : www.ihes.fr

INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES

Institute’s identity; it also enjoys close proximity to a number ofscientific institutions, their cooperation reinforced with thesetting up of the Paris Saclay Campus. The Fondationmathématique Jacques Hadamard was created alongside theCampus, under the aegis of the Paris Saclay Foundation forScientific Cooperation. Its aim is to reinforce research capacityin fundamental mathematics and its interfaces. IHÉS is one ofits founding members, together with Université Paris-Sud 11,the CNRS, École polytechnique and École NormaleSupérieure de Cachan. The new organisation should makethe area even more attractive to mathematicians on theinternational scene.As well as forging links with neighbouring research institutions,the Institute continues to reach out to the public in France andabroad.Encouraged by the success of the book,The Unravelers,Mathematical Snapshots, the Institute organised a day ofconferences in the France Pavilion at the ShanghaiWorld Expoin October 2010.Following on from this event,The Unravelersphoto exhibition is currently touring many Chinese towns,thanks to the Alliances Françaises network. Other projects arein hand, such as “The UnravelersTour in France”,which I hopewill meet with great success.

Jean Pierre Bourguignon

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kaleidoscopic viewof modern mathematics

“The conference made it possible for the journal’s editors and some of its recent authors tomeet. Presentations covered a wide range of topics, from mathematical physics to arithmetics.Some presentations were made by the editors, others by authors who had recently hadarticles accepted by the journal; Gérard Laumon’s presentation on the “fundamentallemma” belonged to both categories.This was an interesting experience and we hope thatit helped to confirm and communicate the wish to broaden the thematic scope of the journal,which was behind the constitution of the new editorial team.”

CCllaaiirree VVooiissiinn

tribute to Lagrange andPoissonThe conference was organised by Jean-Pierre Bourguignon, Pierre Cartier and Yvette Kosmann-Schwarzbach (École Polytechnique), from 24 to26 March 2010 at IHÉS to commemorate the200th anniversary of the publication of importantwork by Joseph-Louis Lagrange and Siméon-Denis Poisson.

nonlinear waves and dispersionOne year after an IHP trimester on this topic,which had been very successful, Frank Merle(Université de Cergy-Pontoise – IHÉS Chair) andFabrice Planchon (Université Paris 13) organiseda meeting where young speakers featured prominently, from 21 to 23 June 2010 at IHÉS.

summer school 2010The second IHÉS French-Asian summer school,which took place from 19 to 30 July 2010, dealtwith Singularities in Partial Differential Equations.The next summer school will be organised atIHÉS in July 2012. Summer schools are entirelyfunded by the Société Générale Fund at IHÉS.

graduate course ED107On Thursdays in February and March 2011,Pierre Vanhove gave a course on PerturbativeCalculation in Quantum Gravity to young doctoral students of the Paris region.www.ihes.fr/~vanhove/cours-gravite.html

inauguration of theHadamard Foundation

The inauguration celebration of theFondation mathématique Jacques Hadamard(FMJH) took place on 17 and 18 May 2011;in the morning of 17 May, it was held atUniversité Paris-Sud 11, in the presence ofValérie Pécresse, French Minister of HigherEducation and Research, and in the afternoon of 18 May it took place at Écolepolytechnique, in the presence of around 200 students.The Foundation was created on 2 February2011, following capital endowment from the French State, as part of the nationalCampus operation. The work of the Foundationwill be to help the decompartmentalisation of both institutions and research themes, and also to promote international activites.Various practical measures have already

been taken, such as international scholarshipprogrammes at masters and postdoc levels andsupport for conferences.Partnership agreements are also being signedwith major science education and traininginstitutions in PR China.

Valérie Pécresse, Université Paris-Sud, 17 May

Alain Connes

Claire Voisin and Sergiu Klainerman becamethe managing editors of Les PublicationsMathématiques de l’IHÉS on 1st January 2010.

They organised the first ever PublicationsMathématiques meeting, Kaleidoscopic view ofmodern mathematics, from 8 to 10 January2011. IHÉS hosted the event on 8 January. Itwas a great day of conferences given in turnby Horng-Tzer Yau, Gerhard Huisken, AlainConnes and Cédric Villani. The next two daysof conferences on 9 and 10 January took place at the Institut Henri Poincaré, and sawpresentations made by: Tom Mrowka, Jean-Yves Welschinger, Jean-Pierre Demailly,Philippe Biane, Pierre Raphaël, HirakuNakajima, Benjamin Enriquez and GérardLaumon.

CARMINThe Institut Henri Poincaré (IHP), CIRM(Centre International de Rencontres Mathé-matiques ), ICPAM (International Centrefor Pure and Applied Mathematics) andIHÉS submitted a project, called CARMIN, for the reinforcement of theircooperation, in response to the call for“LabEx” (laboratories for excellence) proposals, which is one of the elements ofthe “investments for the future” to be fundedby the French State’s national loan. Theseinstitutes represent collective tools whichcontribute to the French mathematicalcommunity’s international visibility.

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events

three string generations at IHÉS“String theory is the interdisciplinaryscience, which combines methods and goalsof physics and mathematics. One of theambitious goals of string theory is toconstruct the fundamental theory of nature, combining quantum field theoryand the theory of general relativity. Ideas originating in string theory find unexpectedapplications in mathematics, the most notable being the discovery of mirror symmetry, linking (complex) algebraicgeometry and symplectic geometry. Mirrorsymmetry provides the mechanism for thegeometric Langlands correspondence andgives the solution to the Schubert problem,the deformation quantization, the categorisation of the theory of knot invariants, the correspondence between twodimensional conformal field theories andrefined Donaldson theory, to name just afew.”

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Paris-Tokyo arithmetic geometry seminars

Conference organised at IHÉS from 16 to 20 May 2011 by Maxim Kontsevich, Nikita Nekrasov and Gabriele Veneziano, the aim ofwhich was to celebrate the unity and diversityof modern theoretical and mathematical physics.

The idea for this event was also to bringtogether three generations of string theoryspecialists. At the centre, the second generation,born in 1960-1962, represented in thisconference by Nathan Berkovits, RobbertDijkgraaf, Michael Douglas, Igor Klebanov,Gregory Moore, Hirosi Ooguri, SamsonShatashvili, Cumrun Vafa, Erik and HermanVerlinde. With them, the two othergenerations: their advisers, the string theorypioneers, and their students. This internationalconference was supported by FoundationCompositio Mathematica, the RichardLounsbery Foundation, the Collège de Franceand the Fédération de Recherche InteractionsFondamentales (FRIF).

The Paris-Tokyo Arithmetic GeometrySeminar is a video-seminar jointlyorganised between IHÉS and theUniversity of Tokyo since 2010 by AhmedAbbes (IHÉS-CNRS), Christophe Breuil(CNRS-Université Paris-Sud), TakeshiSaito (University of Tokyo), Atsushi Shiho(University of Tokyo) and Takeshi Tsuji(University of Tokyo). It takes place once amonth, with speakers alternately from Parisand Tokyo.A session took place on Wednesday 11 May2011. The speaker was Michel Raynaud(Université Paris-Sud) who gave apresentation from IHÉS on “Permanencefollowing Temkin”. On this occasion, theorganisers and participants in Parisexpressed their sympathy to the victims ofthe recent devastation in Japan and sent a

message of support and friendship to theirJapanese colleagues. IHÉS joins them inexpressing wholehearted solidarity with theJapanese people. The last session of the Paris-TokyoArithmetic Geometry Seminar took placeon Wednesday 15 June 2011. The speakerwas Tomoyuki Abe (IPMU, Tokyo), whogave a presentation from Tokyo on“Product formula for p-adic epsilonfactors”.Other joint IHÉS and University of Tokyoprojects are planned for next year, includingthe “Arithmetic Geometry Seminar inTokyo” conference, which will take placefrom 4 to 8 June 2012.

Cumrun Vafa

Ahmed Abbes

Connes, with whomhe formed a sincerefriendship. His work focuses today onunderstanding theanalytical structure ofamplitudes in quantumfield theory usingmixed Hodge structuresand on the use ofmatroids in spin fieldtheories.All those who have known him at the Institutewill remember the 10 years he spent at IHÉSas a long term CNRS visitor very fondly. Wewish him every success in his new post.

“Friendly Isolation

When I returned toEurope in the mid90s from two postdocyears spent at theUniversity of Hobart,Tasmania, I returnedwith many cherishedmemories of loneliness

well spent: over there, solitude to thinkwas provided in spades.When I arrived five years later at IHÉS,I found that cherished sense of isolationagain, but in much gentler beautifullycultivated surroundings: the ability toisolate yourself with your thoughts, in themiddle of an intellectual epicenter ofthoughtful reflection, is now the souvenirI will take with me from IHÉS.Thanks to Alain for his friendship, andthanks to all at IHÉS for a wonderfuldecade in my scientific life.”

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awardsprofessors

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Dirk Kreimer, Alain Connes

arrival of Ahmed Abbes

departure of Dirk Kreimer

Ahmed Abbes joinedIHÉS on 1 May 2011as a long term CNRSvisitor. The Institute is very pleased to welcome this talented and dynamicmathematician. A co-organiser of theParis-Tokyo arithmetic

geometry seminars, he is behind the new“Arithmetics and Algebraic Geometry Course atIHÉS” (see 2011 events page 16).

Dirk Kreimer received a von Humboldt Professorship in 2010. This award is given bythe Alexander von Humboldt Foundation, following a nomination by a German researchinstitution. It is the most prestigious scientificaward in Germany.

Following this award, Dirk Kreimer has joinedthe Humboldt University of Berlin, where heleads the new Interdisciplinary Centre forMathematical Physics and focuses on theinteractions between mathematics andtheoretical physics.Dirk Kreimer came to France in 1991intending to enter into regular contact withmathematicians interested in perturbativequantum field theory. His approach torenormalisation using Hopf algebras led himto work from the end of the 1990s with Alain

Ahmed Abbes is a mathematician specialised inarithmetic geometry. He studied at the ÉcoleNormale Supérieure in Paris from 1990 to 1994.With a PhD in mathematics obtained in 1995 atUniversité Paris-Sud, he became a postdocresearcher at IHÉS in 1996. He was subsequentlyappointed CNRS research associate at UniversitéParis 13, then CNRS research director atIRMAR (Université de Rennes 1) from 2007.Ahmed Abbes mainly studies geometrical andcohomological properties of bundles on varietieson perfect fields of characteristic p>0 or on p-adic fields designed for applications in

arithmetic and algebraic geometry. His jointwork with Takeshi Saito (University of Tokyo)enabled a significant breakthrough in the theoryof ramification .He is the author of a treatise presenting asystematic development of rigid geometryfollowing M. Raynaud’s approach, based onformal schemes up to admissible blow-ups.Ahmed Abbes received the CNRS bronze medalin 2005.

departure of Christophe BreuilChristophe Breuil, who came toIHÉS in 2002 as a CNRS longterm visitor, moved to the Mathematics Department at Université Paris-Sud in September2010.A mathematician specialised inalgebraic geometry and numbertheory, his research is on all aspects of the p-adic Langlands

programme, which he started, withseveral researchers now working onit. With his students, he is looking todevelop this programme for groupsother than GL2(Qp), specificallyGL2(F) with [F:Qp] > 1. He receivedthe Grand Prix Jacques Herbrandfrom the Académie des Sciences deParis in 2002. We also wish himevery success.

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professors

Amaldi medalThibault Damour was awarded the Amaldi Medalduring the 19th SIGRAV conference (Italian Societyfor General Relativity and Gravitation) which took place in Pisa (Italia) from 27 September to 1st October 2010.

Royal Irish Academy gold medal

Peano prizeDavid Ruelle, honorary professor at IHÉS, received the 2010 Peano Prize on 18 November2010 in Turin, for his book La mente matematica(Ed. Dedalo), translated from the original Frenchversion, which was published in 2008,L’étrange beauté des mathématiques (Ed.Odile Jacob).

Compositio MathematicaprizeThe Compositio Mathematica Foundation haschosen to award the first Compositio Mathe-matica Prize to Nikita Nekrasov, Davesh Maulik, Andrei Okounkov and Rahul Pandharipande for their article Gromov-Witten Theory and Donaldson-Thomas Theory II (Compositio Math.142 (2006), 1286-1304). This prize was awarded during the CompositioPrize Festivity at Amsterdam University on 2 July 2010.

Thibault Damour, knight of the Legion of Honour

Thibault Damour received the insignia ofknight of the Legion of Honour on 6 December2010 during a ceremony organised at IHÉS.

His friend Philippe Starck came to confer thedistinction, as the two men have known eachother for ten years and each holds the other ingreat admiration. Here is an extract from the coulourful speech given by Philippe Starck onthis occasion:“We tried to meet regularly over the course ofa few years so that he could teach me things.It was extraordinary! He talked about quantum ..., strings (…) Ididn’t understand anything. But actually, thepoint wasn’t that I understood or not, becausewhat was important for me was to hear themusic, because I think there is a music toscience. (...)I also think that, if we’re sensitive, there is obviously poetry, a poetry of mathematics, a

poetry of science and that poetry is transposablein real life. And I live much better todaythanks to the little I have understood by osmosis, in a very varied way, in a very verypersonal way and I thank him for that.”

Thibault Damour, Philippe Starck

Samson Shatashvili, theoretical physicist, professor at Trinity College, Dublin and LouisMichel Visiting Chair holder at IHÉS since 2000,received the Royal Irish Academy Gold Medalon 24 November 2010, in recognition of hisseveral groundbreaking discoveries in the fieldsof theoretical and particle physics.

Mikhail Gromov

Laurent Lafforguehonorary doctorThe University of Notre Dame, Indiana,United States, awarded Laurent Lafforgue,IHÉS permanent professor, the title of honorary doctor on 22 May 2011. On that occasion, he made two scientific presentations on the Langlands programme,a topic he has been working on for manyyears, and gave a public conference entitled“Does basic research have meaning? A fewremarks by a catholic mathematician”.

Mikhail Gromov, ForMemRSMikhail Gromov was elected Foreign Memberof the Royal Society (United Kingdom) on 20 May 2011. With this distinction, The RoyalSociety recognises Mikhail Gromov as one of“the most deeply original mathematiciansof our time”.

Mikhail Gromov joins the ten or so greatFrench scientists who have also been electedRoyal Society Foreign Members, amongwhom are Jean-Pierre Serre, Jacques Friedel,Edouard Brézin and, more recently, PascaleCossart.The Royal Society has around 140 ForeignMembers across all disciplines out of a total ofaround 1450 Fellows. They are elected for lifethrough a peer review process; eight new Foreign Members are elected each year.

This article focuses on the description of thelast few orbits before coalescence of binaryneutron star systems and their experimentalobservation (which hopefully will happensoon) by the network of gravitational wavedetectors LIGO / VIRGO - LIGO is in theUnited States and VIRGO is the French-Italian gravitational wave detector installed inCascina, near Pisa.The main result of the article is to have shownthat the new analytical description (called“effective one body” or EOB) of the dynamicsof binary systems, invented at IHÉS a few yearsago (by Alessandra Buonanno and ThibaultDamour) and recently developed at IHÉS byThibault Damour and Alessandro Nagar, canbe used to describe the gravitational signalemitted by the last orbits of a system of twoneutron stars with a precision adequate fordetection by LIGO / VIRGO.

the Schlumberger Chairpublication

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description of the last orbits of binary neutron star systems

The relativistic gravity theorists, ThibaultDamour and Alessandro Nagar, with a teamfrom the Albert Eintein Institute, Germany,have greatly advanced the description of thefinal orbits of binary systems of neutron stars.

An article describing this discovery waspublished by Physical Review Letters (PRL):Analytic Modelling of Tidal Effects in theRelativistic Inspiral of Binary Neutron Stars,Phys. Rev. Lett 105, 261101 (2010).This article is the result of a collaborationbetween a team of relativistic gravity theorists,Thibault Damour, permanent professor atIHÉS, and Alessandro Nagar, visitingresearcher at IHÉS, and a team of “numericalrelativity” specialists (all formerly together atthe Albert Einstein Institute, a Max-Planckinstitute located in Golm, Germany) currentlyworking in several institutions: Luca Baiotti(Osaka and Kyoto Universities, Japan), BrunoGiacomazzo (University of Maryland andNASA Goddard Space Flight Center, US) andLuciano Rezzolla, head of the numericalrelativity group of the Albert EinsteinInstitute.

The paper also shows that this detection willallow the measurement of the ratio betweenthe mass and radius of neutron stars. Thismeasure is potentially very important becauseit will give access to new information on theequation of state of ultra-dense nuclear matter,of which neutron stars are made. The results ofthis article were obtained by comparing thepredictions of the IHÉS analytical methodwith the best (and to date longest) numericalsimulations (on supercomputers) of thegravitational wave signal emitted by binaryneutron star systems. These numerical resultshave been obtained recently thanks to thenumerical methods developed at the AlbertEinstein Institute.

Illustrations: numerical simulation of the last orbits of a binary neutron star system.Credits: B. Giacomazzo (AEI), R. Kaheler (ZIB/AEI), L. Rezzolla (AEI)

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the Schlumberger Chair

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Background to theSchlumberger Chair

The sources of inspiration for theoreticalsciences are many: questions lying,sometimes for centuries, at the veryfoundation of sciences (such as in thecreation of non-Euclidean geometries),problems arising from the developmentof high technology (such as seismicstudies leading to the definition ofwavelets), or concepts originating inneighbouring sciences (such as thesystematic consideration of non-commutativity in mathematics stimulatedby the success of quantum mechanics).In the past few years, IHÉS has started toexplore new sources of inspiration, suchas high technology and biology, whilemaintaining its fundamental values:freedom of research, quest for excellence,interdisciplinarity, and also human andscientific diversity. Schlumberger Ltd.was a natural partner for a project onissues at the interface with appliedresearch and of more direct interest tocompanies. Schlumberger Ltd. is a hightechnology company, whose productsand services draw extensively from manyscientific domains: physics, chemistry,geology, geophysics and mathematics. Inmany of these fields, the rigor necessaryto innovate requires the knowledgecreated at the frontiers of fundamentalresearch. Schlumberger has a tradition ofdeep interaction with the scientificcommunity by locating its laboratories inclose proximity to strong academicinstitutions, while maintaining a largeinternal research effort.

“Joining the Schlumberger Chair was forme a unique opportunity to build asustainable and productive relationship ofhigh-level research between my universityin Stanford and IHÉS. Our current andpast students and our close collaborators inFrance and the United States will benefitgreatly from working with us, JosselinGarnier and me, on research projects thatare both innovative and interdisciplinary.We are already engaged on work onimaging, propagation of uncertainty andsystemic risk. I am very satisfied with theprogress on these issues in such a shortperiod.”

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Philippe Lacour-Gayet

“The proposal of a six-month term to holdthe Schlumberger Chair was perfect for me:it came at a time when I was highlymotivated and intr igued by innovativetypes of research around imaging. The beliefthat IHÉS would provide the environmentto develop these tracks was immediatelyattractive. Finally the idea of working withGeorge Papanicolaou on these issues onlystrengthened this conviction. So I couldonly accept the proposal with enthusiasm. The first few months, with many results onimaging and other issues that have emergedover the course of my discussions withGeorge Papanicolaou, fully satisfy me.They encourage me to believe that thissemester is the beginning of an active andprolific per iod between IHÉS, StanfordUniversity, the Université Paris Diderotand École Normale Supérieure, where Iwill be giving courses in the second semesterand hosting a working group.”

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inaugurationJosselin Garnier and George Papanicolaouare the first holders of the SchlumbergerChair for Mathematical Sciences at IHÉS.From September 2010 to February 2011,they worked together on imaging projects.More specifically, they worked on a newtype of robust beamforming method incomplex media and on the improvementof resolution in imaging with indirectlighting resulting from the heterogeneitiesof the medium. They have developed and analysedmathematical models to estimate thesystemic risk of a large number ofinteracting agents each trying to spreadtheir individual risk. They have alsoinitiated a study of propagation ofuncertainty for a classic problem ingeophysics, which consists in estimating thespeed of surface waves from themeasurement of travel times (see article p. 8).

The Schlumberger inaugural conferencewas held on 17 and 18 November 2010 atIHÉS. The theme chosen and presented byJosselin Garnier, Habib Ammari, PatrickJoly, Felix Otto, Grégoire Allaire andGeorge Papanicolaou was “MultiscaleMethods and Imaging”.Inaugural lectures by the first two holdersof the Chair were given in the evening of18 November. George Papanicolaou andJosselin Garnier presented with great claritythe work they have undertaken as part ofthe Schlumberger Chair, demonstrating thevalidity of creating this Chair at IHÉS. Theresulting collaboration will be of benefitboth to the scientific community and theworld of industry.

imaging with noisestep of a typical time-reversal experiment, apoint source emits a short pulse that propagatesin a homogeneous or heterogeneous medium(see Figure 1). The time-reversal mirror is usedas an array of receivers that record the wavesignals. In the second step of the experiment,the time-reversal mirror is used as an array ofemitters that re-emit the time-reversedrecorded signals. The waves then propagateback into the medium. Due to the timereversibility of the wave equation it is expectedthat the wave refocuses on its original sourcelocation. What was not so expected is that therefocusing is better when the medium is

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In sensor array imaging waves are used toprobe an unknown medium. Different wavetransmission and reception modalities can beimplemented depending on the applications:non destructive testing, medical imaging,seismology. Travel time tomography,backpropagation or migration are well-knowntechniques to extract information from thearray data. Recently new ideas have emergedfrom experimental observations such as super-resolution effects in time-reversal experimentsor from theoretical concepts such as coherentinterferometry or cross correlation methods. Inparticular the possibility to use uncontrolledambient noise sources instead of controlledactive sources has attracted a lot of attentionespecially in seismology. In this article we givea brief overview that explains the connectionbetween these different ideas and we give therecent results obtained during our semester atIHÉS.

Time-reversal Experiments. Time reversalexperiments were first carried out by MathiasFink and his group in Paris. They were donewith ultrasonic waves and have attractedconsiderable attention because of thesurprising effects of enhanced spatial focusingand time compression in random media [Fink,Scientific American 281 (1999), 91]. A time-reversal experiment is based on the use of avery special device: the time-reversal mirror. Itis a collection of transducers that can be usedeither as emitters or as receivers. In the first

randomly heterogeneous than when it ishomogeneous. The mathematical analysis ofenhanced time-reversal refocusing in randommedia has revealed that the time-reversalexperiment can be interpreted as a correlationmachine [1]: in the second step of the time-reversal experiment, the time-reversed waverevisits the same medium as the one that wasprobed during the first step of the experiment,and this is a key point. If the medium duringthe second step is exactly the same as the oneduring the first step, then the scattering withthe heterogeneities of the medium canproduce multi-pathing that builds up in acoherent way to produce a sharp focusing atthe original source location. If the mediumduring the second step is not exactly similar tothe original medium, then refocusing becomespoor and unstable. In practice, the enhanced spatial focusing andtime compression of signals in time reversal inrandom media (see Figure 2) have manydiverse applications in detection and in focusedenergy delivery on small targets as, for example,in the destruction of kidney stones. Enhancedspatial focusing is also useful in sonar andwireless communications for reducinginterference. Finally time reversal ideas haveplayed an important role in the developmentof new methods for imaging in random mediaas described below.

Coherent Interferometric Imaging. Themathematical analysis of time-reversal

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y

TRM

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TRM

FIG. 1: Ideal time-reversal experiment, with atime-reversal mirror (TRM) that completely surrounds the region of interest. The left pictureplots the first step of the experiment. A point sourceat y emits a short pulse that propagates through themedium and is recorded by the time-reversal mirror.The right picture plots the second step of the time-reversal experiment. The time-reversal mirror re-emits the time-reversed recorded signals that propagate back into the medium and refocus at theoriginal source location.

George PapanicolaouRobert Grimmett Professor in Mathematics, Department of Mathematics, Stanford University, since 1993, after spending much ofhis career at the Courant Institute for Mathematical Sciences at NewYork University, he has received numerous prizes and awards, the twomost recent being: William Benter Prize in Applied Mathematics 2010and Josiah Willard Gibbs Lecture, 2011.

Josselin GarnierEducated at the École Normale Supérieure in Paris, he is professor ofmathematics at Université Paris Diderot where he conducts his researchin the Laboratoire de Probabilités et Modèles Aléatoires and in the Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie. His main research interest is related to waves in random media. He received the Felix Klein Prize in 2008.

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backpropagating numerically the recordedsignals, that are supposed to refocus on thelocations of the main reflectors present in themedium, as is observed in time-reversalexperiments. This imaging method is very efficient whenthe medium is homogeneous or perfectlyknown, since it is then strictly equivalent to atime-reversal experiment in which thebackpropagation is carried out numericallyinstead of physically. However, when themedium is heterogeneous and not perfectlyknown one has to backpropagate the recordedsignals in a fictitious medium that is not thereal one, and poor refocusing is observed.Coherent interferometric imaging is based onthe backpropagation of local space-time crosscorrelations of array data and was introducedin order to improve images when the mediumbetween the array and the object to be imagedis inhomogeneous and unknown [Borcea et al.,Inverse Problems 21 (2005), 1419]. During oursemester at IHÉS we have shown that thecoherent interferometric imaging is in factequivalent to a windowed beamformer energyfunction, that is, a quadratic function thatinvolves only time gating and time delayingsignals in emission and in reception. In thisform coherent interferometric imaging can beimplemented efficiently both in hardware andsoftware, at a computational cost that is, ideally,comparable to the usual beamforming andmigration imaging methods. We have alsorevisited the trade-off between image stabilityenhancement and loss of resolution from thepoint of view of its equivalence to a windowedbeamformer energy imaging function [3].

Ambient Noise Imaging. The geologicalstructure of the Earth can be explored byobserving the propagation of elastic waves inthe Earth crust. In classical seismology only thewaves generated by earthquakes or by artificialexplosions and recorded by a network ofsensors (geophones) are used. Time-reversalexperiments or active array imaging (usingarrays of sources) are not possible inseismology since controlled sources of seismicwaves are difficult to construct. However, evenwithout any earthquake or explosion, a weakincoherent signal is recorded by seismographs:the seismic noise, whose frequencycomponents around 0.1Hz consist mostly ofsurface waves produced by the interaction ofthe ocean swell with the coast. It turns out thatthese noise signals can be used to obtain travel

time information. The main observation is thatthe cross correlation of the noise signalsrecorded at two sensors is related to the traveltimes between the sensors. As a consequence,the background speed of propagation can thenbe obtained from the estimated travel timesbetween sensors in a network covering theregion of interest, as was done in the SouthernCalifornia region [Sabra et al., Geophys. Res.Lett. 32 (2005), L14311]. In fact the idea ofexploiting the ambient noise and using the

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FIG. 2: Time compression of signals in time reversalin random media (numerical simulations). The toppicture plots the first step of the experiment. Eachline is a snapshot of the wave profile at differenttimes. The bottom blue line is the initial condition:a left-going wave is incoming from the lefthomogeneous half-space and enters thehetererogeneous region. The black lines plot thewave profile as it propagates in the heterogeneousregion. The top red line plots the reflected wave thatis recorded by the time-reversal mirror. The bottompicture plots the second step of the time-reversalexperiment. The bottom blue line is the initialcondition: it is the signal recorded at the end of thefirst step that is time-reversed and re-emitted by thetime-reversal mirror. The top red line plots thereflected wave, which shows that a time-compressedsignal emerges from the medium.

FIG. 3: Coherent interferometric imaging. In the leftpicture a sensor array is used to probe an unknownmedium in which reflectors are buried (one of thetransducer is used as a source, the other transducersare used as receivers and record the echoes, whichform one column of the array response matrix). Inthe right picture local cross correlations of recordedsignals are backpropagated numerically and focusmore or less on the locations of the reflectors.

experiments has shown that the crosscorrelation of partially coherent waves is animportant object. A new imaging method wasthen proposed in the context of sensor arrayimaging in random media. When imaging with waves the unknownmedium is probed with waves emitted from aset of sources and then the echoes are recorded

cross correlation of noise signals to retrieveinformation about travel times was firstproposed in helioseismology [Rickett et al.,The Leading Edge 18 (1999), 957]. It has beenapplied to background velocity estimationfrom regional to local scales, volcanomonitoring, and petroleum prospecting[Larose et al., Geophysics 71 (2006), SI11]. These observations have motivated novel ideasfor imaging. First of all one can explainmathematically the relation between crosscorrelations of noise signals and the travel timebetween the two points. This is motivated bythe analogy between the cross correlation ofthe noise signals and a virtual time-reversalexperiment in which one of the points is theoriginal source, the other point is the receiver,and the noise source locations play the role ofthe virtual time-reversal mirror. This analogy(together with the Helmholtz-Kirchhoffidentity, a variant of Green’s identity) showsthat, when the support of the random noisesources completely surrounds the region ofinterest, then the cross correlation of therecorded signals has a peak at the travel timebetween the sensors (see Figure 4). In manyapplications, however, the noise sourcedistribution is spatially limited and the wavesrecorded by the sensors are dominated by the

at a set of receivers. In classical array imagingthe data are collected in the form of the arrayresponse matrix (see Figure 3). The arrayresponse matrix is obtained column by columnby emitting a pulse from each source locationat a time and then recording the echoes at allthe receiver locations. Then the recordedsignals are processed to generate an image atsearch points (pixels) in the image domain ofinterest. This processing consists in

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flux coming from the direction of the noisesources. The cross correlations of the recordedsignals then depend on the orientation of thesesensors relative to the direction of the energyflux. This affects significantly the quality of theestimate for the travel time. As can beexplained by stationary phase arguments, it isgood when the line between the sensors isalong the direction of the energy flux and badwhen it is perpendicular to it. When there is multiple scattering in themedium, as in an ergodic cavity or as in arandomly inhomogeneous medium,directional diversity of the recorded signals isenhanced by multi-pathing. This was studiedin the context of time-reversal experimentsand it has been shown that time-reversalrefocusing can be enhanced in a randomlyscattering medium. It turns out that it ispossible to exploit the enhanced directionaldiversity of the multiply scattered waves fortravel time tomography using crosscorrelations of ambient noise signals. Indeedthe travel time between two sensors can beestimated even in unfavorable situationsprovided that special fourthorder correlationfunctions with auxiliary sensors are used[Stehly et al., J. Geophys. Res. 113 (2008),B11306]. By unfavorable we mean that themain component of the energy flux from thenoise sources is roughly perpendicular to theray connecting the two sensors. The fourth-order correlations can be used effectively forenhancing travel time estimation between thetwo sensors by exploiting the scatterers assecondary sources and by reducing thecontribution of the primary flux. Ambient noise signals can also be used forpassive sensor imaging of reflectors embeddedin the medium. Indeed, in the presence ofreflectors, the cross correlations between anytwo sensors have, in addition to the main peaksat the travel times between them, other peaksat lag times related to travel times from thesensors to the reflectors. The analysis of therelation between the secondary peaks in thecross correlations and travel times betweensensors and reflectors shows how to image thereflectors by suitably migrating the correlations[3]. The resolution of the image depends onthe directional diversity of the noise signalsrelative to the sensor array and on the reflectorlocation. When directional diversity is limitedit is possible to enhance it by exploiting thescattering properties of the medium. However,scattering increases the fluctuation level of the

cross correlations and therefore blurs theimage. During our semester at IHÉS we havestudied the trade-off between resolutionenhancement and signal-to-noise ratioreduction due to scattering [4] and we haveshown that it requires a deep understanding ofwave propagation in random media and scalingissues. Following the coherent interferometricimaging ideas developed for broadbanddeterministic pulses, it is possible to formspace-time local cross correlations of the crosscorrelations and migrate them. The use ofiterated cross correlation can enhancedramatically the quality of the images (seeFigure 5). These techniques are new and couldcertainly be improved and extended to otherareas, such as microwave imaging, and they canin turn trigger new ideas in active arrayimaging.

0 50 100 150 200−50

0

50

x1

xN

zr

z

x

FIG. 5: Reflector imaging using signals generatedby ambient noise sources (numerical simulations).The configuration is plotted in the top picture: thecirc les are the noise sources, the squares are the scatterers, the tr iangles are the sensors, and the diamond is a small reflector. The image obtained bymigrating the matr ix of cross correlations of the recorded noise signals is plotted in the left bottompicture. The image obtained by migrating specialfourth-order cross correlations is plotted in the rightbottom picture.

x y

0 100 200 300 400 500 600 700 800 900 1000t

piece of signal recorded at x

0 100 200 300 400 500 600 700 800 900 1000t

piece of signal recorded at y

−500 −400 −300 −200 −100 100 200 300 400 5000τ

cross correlation x − y

FIG. 4: Ambient noise imaging (numerical simulations). When the spatial support of the noisesources (circles) extends over all space then the crosscorrelation of the signals recorded at x and y is symmetric and exhibits two peaks that are centeredat plus and minus the travel time between the twopoints.

For further reading:

[1] L. Borcea, J. Garnier, G. Papanicolaou, and C. Tsogka, Coherent interferometr ic imaging,time gating, and beamforming, to appear in In-verse Problems.[2] J.-P. Fouque, J. Garnier, G. Papanicolaou, andK. Sølna, Wave propagation and time reversal inrandomly layered media, Springer, New York,2007.[3] J. Garnier and G. Papanicolaou, Passive sen-sor imaging using cross correlations of noisy si-gnals in a scattering medium, SIAM J. ImagingSciences 2 (2009), 396-437.[4] J. Garnier and G. Papanicolaou, Fluctuationtheory of ambient noise imaging, to appear inCompte Rrendu Acad. Sci. Paris Geosciences.

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In March 2008, IHÉS officially launched itssecond international fundraising campaign,carried out in France, the United States, Japanand China.

This major donor campaign will close at the end of the year ; the Institute intends to make use of these last few months tomaintain its level of commitment and attractnew donors. Looking to the United States, theconsolidation of the Friends of IHES, Inc.organisation bodes well in that respect. In2010, the organisation’s Board changed withthe election of its new President, in the personof Renaud Dutreil. This appointment enablednew elected members to join the “Friends”Board, all very enthusiastic about IHÉS andkeen to increase the organisation’s visibilitywithin New York business circles. Therecruitment of an Executive Director will also

It nevertheless remains important for IHÉS tohave new institutions supporting it: strategicobjectives are yet to be met, such as recruitinga sixth permanent professor or consolidatingthe Institute’s attractiveness at the internationallevel.

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final year for the campaignenable the organisation to engage in sustainedfundraising efforts, especially through theorganisation of events, which are key topromoting the work of “Friends”.Efforts made towards China led to a fewencouraging results. The Institute’s visibility hasincreased there, but progress in the search forChinese donors to the Chern Fund is slow.Fundraising in France has been very successful,with a large increase, since the previouscampaign, in the number of Frenchorganisations among the Institute’s majordonors: several large companies supported theInstitute with very significant contributions.

“On 19 May 2011, the Institute organised a ceremony inhonour of Jean-Paul Gimon whoplayed a key role at a difficult time for IHÉS. The Institute wanted toexpress its profound gratitude tohim through the creation of a Chair.He was in fact the person who encouraged the Institute to undertakeits first fundraising campaign andprovided the resources to make thatcampaign a reality. That was back in 2000, and IHÉS was experiencinga worrying financial situation. Since then, over 30 million euros has beenraised in France and worldwide. This is thanks also to new key figures whohave rallied to the IHÉS cause. In this regard, I would like to thank Renaud Dutreil, Chairman of LVMH Inc., who has agreed to take overin representing Friends of IHES, Inc. in the United States, setting up aneffective team and making “Friends” a very dynamic organisation, whichplays an important role in the Institute’s international influence.As Chairman of the Board of Directors of IHÉS, I also welcome the commitment of new institutions to the Institute, and particularly HuaweiTechnologies France, who recently made a significant gift to IHÉS.Other sources of satisfaction are the numerous awards received by IHÉSprofessors, but also efforts made in recent past years to improve the Institute’svisibility through creative initiatives such as the public conference held at the World Expo in Shanghai or the book, The Unravelers, MathematicalSnapshots. Without this enhanced visibility, the 50th Anniversary Campaign would not have been so successful.”

PPhhiill iippppee LLaaggaayyeettttee

the 50th Anniversary Campaign

Jean-PaulGimonChair

Created in 2005in memory of

Jean-Paul Gimon, former member of theIHÉS Board of Directors, and a highlyvalued adviser for the Institute as it launched its first ever fundraising campaign in 2001, this Chair will providepermanent funding for two months ofresearch visits at the Institute each year.Jean-Paul Gimon was always mindful ofmaking a place like IHÉS accessible toyoung people and in particular to thosefrom developing countries; for this reason, the Chair bearing his name is intended for young people, with thepriority given to researchers from Africa.

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Support from CIC The New York subsidiary of CIC haslong been a supporter of the work carriedout by Friends of IHES, Inc. thanks toSerge Bellanger, who was a fervent admirer of IHÉS and of the excellence ofFrench mathematics. Friends of IHES,Inc. is very happy to see the partnershipcontinue in 2010 and 2011 and warmlythanks CIC for its support.

conférences et célébrations

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renewal of the Board of Friends of IHES, Inc.

A new campaign has been launched byFriends of IHES, Inc, with a financial target of3 million dollars to be raised in 2011 and2012.

Priority is to be given to securing funding forAmerican visitors, who represent around 30%of the visitor programme at IHÉS. An endowed United States Fund will be setup to provide permanent funding for some ofthe American visiting researchers. In addition,

campaign in the United States

11 years into its existence, theorganisation has elected a new Presidentand three new members.

Friends of IHES Inc. was set up in 1999mainly to help IHÉS increase its visibilityin the United States. There are historicallinks between IHÉS and the United States,going right back to the very early days,when Léon Motchane convinced RobertOppenheimer to join the Institute’s Boardof Directors and to help guide its first steps.Since then, hundreds of Americanresearchers have been invited to theInstitute. Many IHÉS permanent professorshave also contributed to the vitality ofexchanges between the Institute and theAmerican scientific community.

“Like manyothers, I have always placedmathematics atthe forefront ofkey disciplinesand I am proudand pleased to see France – and IHÉS inparticular – taking such a prominent rolein their development, for the furtherance ofscience and intelligence.IHÉS created a unique community of international scientists with significantachievements in mathematics and theoreticalphysics, in an environment of extraordinaryintellectual freedom and independence.The campaign launched in 2011 in theUnited States aims to provide Americanresearchers with new opportunities to workat IHÉS. It is crucial for Friends of IHES,Inc., making a fresh start in 2011, to organise scientific events to reach out tonew US supporters, corporations and foundations willing to support fundamentalresearch in mathematics.Developing exchanges between the UnitedStates and France will contr ibute to theexpansion of academic excellence of bothnations and to the benefit of the world’sscientific community. Supporting this causemeans taking one step closer towards understanding the world.”

RReennaauudd DDuuttrreeiill

2011 - 2012 US campaign

Since its inception, “Friends” has helpedIHÉS considerably in terms of visibility,and also in terms of funds raised and transferred to the Institute. Theorganisation is now a real asset for theInstitute. In May 2010, Renaud Dutreil, Chairmanof LVMH Inc. was elected President of theBoard of Directors of Friends of IHES, Inc.Following this election, new members,who come from the corporate world inNew York, joined the organisation. Thesenew arrivals will hopefully lead to an increase in the activity of “Friends” and improvements in identifying andconvincing new donors.

Friends of IHES, Inc. will be reaching out tofoundations, with a view to entering into newpartnerships aimed at providing multi-annualgrants for the support of American visitors. In a new departure, “Friends” is creating a “Corporate club”, to bring it into closercontact with new American companies, witha number of high profile events, which wehope will soon become well known in NewYork business circles.

Reception at the Ambassador, Permanent Representative of France to the United Nations, Gérard Araud, at the FrenchResidence, New York, on 12 May 2010

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“... Links between the Insitute and the United States are very strong. They were so fromthe start, with the famous Institute for Advanced Study (IAS) in Princeton providing a sortof blueprint for the Institute. These links are just as strong today: the Institute has no fewerthan 30% American mathematicians, physicists, biologists and computer scientists within itsranks. Further reinforcing the links between the Institute and the United States is a key objective for Friends of IHES.This morning, we wanted to br ing together the worlds of finance and mathematics. French mathematicians represent a valued talent pool on Wall Street, and sometimes a controversial one (mathematicians are admittedly easy targets for criticism!).For my part, I am pleased to see that French training and expertise are so appreciated here ...”

EExxttrraacctt ffrroomm PPhhiilliippppee LLaalllliioott’’ss ssppeeeecchh,, CCoonnssuull GGeenneerraall ooff FFrraannccee iinn NNeeww YYoorrkk

“Some New Directions at the Interface between Finance and Mathematics: Bottom-Up Finance” was the theme explored duringthe “Finance breakfast meeting” organised byFriends of IHES, Inc., on 12 May 2011.

The event, which took place in the elegantsetting of the Consulate General of France inNew York, represented anopportunity for scientistsand finance specialists,together with leadingbusiness people, tointeract and exchangeviews on the topicalsubject of financialmathematics, which washeavily criticised afterthe severe financial crisisin 2008.Two scientists, whosework covers both mathematics and finance, madebrief presentations on this topic: EugèneDurenard, Partner, Orion InvestmentManagement Ltd., and Petter Kolm, Director ofthe Mathematics in Finance M.S. Program at theCourant Institute of Mathematical Sciences,New York University.Eugène Durenard made the first of thepresentations, during which he shared histhinking on current developments in financialmathematics. In his view, financial theory haslong been based on a “top-down” approach,which is seen today as having had a disappointing

track record. A change of paradigm is clearlyneeded and the beginnings of it are alreadyemerging. This new approach is multi-facetedand is primarily based on the investigation of themarket as a complex system where large scalepatterns emerge from elementary interactions of reasonably simple agents. It should allow a unified framework to study the various

p h e nomeno l og i c a lfeatures (such as theasymmetric behaviour ofagents or non-linearitiesin macro-economics)that are central to thedesign of efficient and profitable survivalstrategies in the globalmarketplace.Eugène Durenardconcluded his talk byexplaining that the new

direction in mathematical finance should comefrom the confluence of recent research incomplex systems, control theory, autonomousadaptive agents and some aspects of mathematicalbiology.The event was also an opportunity todemonstrate the high quality of events nowoffered by Friends of IHES, Inc.. We hope thatmany other events of this level will be organisedsoon.

finance breakfast meeting at theConsulateGeneral of France in New York

13

conférences et célébrationscampaign in the United States

Yuri Tschinkel, Eugene Durenard

Luc Hardy, David Goldman

Véronique Carpentier, Thierry Simon, Jim Simons

campaign in the People’s Republic of China

14

world expo in Shanghai

The Paris - Île-de-France Pavilion at the WorldExpo, where the travelling exhibition TheUnravelers was shown from 16 to 23 October2010, was the starting point for the exhibition’slong tour across China, via the AlliancesFrançaises network. Nine major cities havechosen to show it between November 2010 andSeptember 2011: Nankin, Canton, Jinan, Xi’an,Beijing, Hangzhou, Chongqing, Macao andTianjin. The publication by Higher EducationPress of the Chinese version of the book, TheUnravelers, complements the exhibition, withtexts by Chinese scientists added to the originalversion. This book, edited in France by ÉditionsBelin, is the work of J.-F. Dars, A. Lesne and A. Papillault.

The Unravelers exhibition

For more than 10 years, IHÉS has beenundertaking projects aimed at increasing itsvisibility within the Chinese scientificcommunity and attracting more Chineseresearchers.

The Shanghai World Expo was a greatopportunity to get in touch with the Chinesepublic, and also with students and researchers.Which was why IHÉS applied to organise aconference in the France Pavilion, “meetingthe Unravelers”, a scientific conference for thegeneral public, consisting in a series of shortpresentations. The conference, which wasinitially planned over a half-day, had to beextended to a full day, to satisfy the manyregistration requests received. In the end, over200 people came to listen to leading scientistswho were there to share some of their currentresearch work or certain aspects ofmathematics that they find particularlyinteresting.Four of the eight presentations dealt withmathematical physics and how geometrycontributes to our understanding of theUniverse: Liu Kefeng (Zhejiang University)Mathematics born of physics, Long Yiming(Chern Institute of Mathematics, NankaiUniversity) The solar system seen by amathematician and Hu Sen (University ofScience and Technology of China) Searching

for the geometry of the universe. Cédric Villani(Université de Lyon I - Institut HenriPoincaré) spoke of how galaxies evolve, usingan analogy from gas kinetics. Other speakerswere: Jean-Pierre Bourguignon (CNRS-IHÉS), Josselin Garnier (IHÉS-Université Paris

Diderot), Li Ta-Tsien (Institut Sino-Françaisde Mathématiques Appliquées), GeorgePapanicolaou (IHÉS-Stanford University).They touched on a wider range of themes,including flexible polyhedra, imaging inseismology, mathematics in finance and thegolden ratio.IHÉS thanks the Consulate General of Francein Shanghai, Yao Yi-Jun and his wife, Xu Mingyu, for their invaluable help andactive contribution to the success of the day, together with the event sponsors: EADS, Saint-Gobain, Société Générale and LCL Banque privée

Exhibition in Xi’an

Li Ta-Tsien

Hu Sen, Liu Kefeng, George Papanicolaou, Josselin Garnier, Cédric Villani

Inauguration of the exhibition in Beijing by Jean-Pierre Bourguignon

passed away, the Chern family hasmaintained its full support to the project.

In November 2010, theChern Foundation made anew additional donation.IHÉS would like to expresswarmest thanks for her trustto May Chu, Shiing ShenChern’s daughter and theFoundation’s President.Another major gift came tothe Institute recently for theChern Fund, from the“Fondation d’entrepriseEADS”. EADS is also one of

the Institute’s long-standing partners. Overthe past ten years, various projects havebeen set up at the Institute thanks to itssupport.

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campaign in the People’s Republic of China

donations for the Chern FundThe Chern Fund is a fund set up to financeChinese scientists invited to the Institute.In providing this support, ithelps meet three broaderobjectives: intensifyingscientific exchanges betweenChina and France,promoting scientific researchwithout any programmeconstraints and increasing the visibility of IHÉS within Chinese scientificcommunities (in mathematics,theoretical physics and at the interface betweenmathematics and biology). Many French companies have become partners of this project; the Institute hopesto also attract Chinese donors and isworking actively to that end.Since its creation in 2002, the Chern Fundhas received the support of ProfessorShiing-Shen Chern who was personallyinvolved in the development of the ChernFund, by making a financial contributionto it, through his own foundation. Since he

Huawei Technologies Fund A new fund set up to finance invited researchersof all nationalities was created by the Frenchsubsidiary of Huawei Technologies at thebeginning of the year.

This Chinese high technology companyhas opened two research centres inFrance, one in Lannion (Brittany) andone in Cergy-Pontoise (near Paris).Since its inception, Huawei Technologies hasalways viewed research as an essential means toimprove its ability to meet market requirements

Leo Sun (Huawei France Managing Director), Jean-Pierre

Bourguignon, François Quentin (Huawei France President),

Philippe Lagayette

but also provide highly innovative technicaltools. Which is why this leading Chinese groupdecided to support fundamental research in

mathematics and chose IHÉS for thatpurpose, both because of the freedomoffered to its researchers and theexcellence of the work carried out there.The Huawei Technologies Fund at IHÉSwill support 2 months of research visits

each year in perpetuity.

Louis Nirenberg (first receipient of the Chern medal) and

May Chu during the International Congress of Mathematicians

at Hyderabad, August 2010

Chern Shiing-ShenChern Shiing-Shen is one of the greatestgeometers of the 20th Century. Hiscontribution to differential geometry inparticular was major, and had multipleapplications. Professor Chern would havecelebrated his 100th birthday in 2011.The Chern Institute of Mathematics,Nankai University (Tianjin, China) andMSRI (Berkeley, United States), twoinstitutes that owe their creation to him,will be organising celebrations from 24to 28 October 2011 (at the CIM) andfrom 30 October to 5 November 2011(at MSRI). IHÉS will be organising a day of conferences in his memory on 17 November 2011.

point of view by ...

Shelly Garion and Sefi Ladkani

We are a married couple of mathematicians currently staying at IHÉS as EPDI laureates. Weboth graduated at the Hebrew University of Jerusalem, Israel. Sefi’s research is in representationtheory and homological algebra and Shelly worksin group theory. Both areas of research are in thegeneral field of algebra, so although each of us carries out his/her research independently, we tryto assist and support each other in generalquestions and issues that arise during our work.In his research, Sefi focuses on the theme of derived equivalence and its combinatorial aspects,especially concerning categories arising fromcombinatorial data appearing naturally in algebraic, combinatorial and topological contexts.Derived categories, and more generally triangulatedcategories, have found applications in diverseareas of mathematics and mathematical physics,forming also bridges between various domains ofalgebra and geometry.Shelly investigates finite simple groups. Finitegroups naturally occur when considering the symmetry of mathematical and physical objects, the finite simple groups can be seen astheir building blocks. She focuses on the study of the combinatorial and probabilistic aspects ofthese groups, utilizing techniques from numbertheory and algebraic geometry.A common aspect of our work is the quite frequent use of computer programs in order toexperiment and check several instances of a

courses in the winter. The surrounding landscapearound the Rhine is particularly pleasant.In 2010 we moved to IHÉS at Bures-sur-Yvette,a small town south of Paris. This quiet and tranquil place has inspiring surroundings allowingone to concentrate on research and think of mathematical problems in the relaxed atmosphereamong the woods of the Bois-Marie forest. Onedoes not have to worry too much about everydaylife here, as the staff of IHÉS takes care of manyaspects. Accommodation is provided at the wellequipped Ormaille residence, and lunch is servedat the cafeteria allowing also informal interaction among researchers.Nevertheless, IHÉS is close enough to Paris withall the possibilities this metropolis has to offer.Professionally, there are many universities so thatseminars, conferences and other activities arebeing held regularly. During leisure time, one canenjoy the cultural and historical gems that Parisis full of. Our stay in Europe provided us with many professional opportunities. We could convenientlytravel in order to participate in scientific meetingsand give talks at various institutions. Easy travelalso facilitated collaboration with other scientistsas personal contact is still important even in ourcurrent digital era.We will always have pleasant memories from the time during our EPDI fellowship. It gave us aunique cultural experience as well as the opportunity to practice new foreign languages.

problem, before formulating claims and assertionswhich are then proved in full generality using rigorous methods.We started our stay in Europe in 2008 by visitingIHÉS for two months and then we moved toBonn. Later, we were both selected as EuropeanPostdoctoral Institute (EPDI) laureates for theyears 2009-11. This is a two-year postdoctoral fellowship allowing one to carry out research atprestigious institutes in Europe. This has severaladvantages at this early stage of the career; it allows to focus on research without many externaldisturbances as well as to establish contacts anddiscuss ideas with researchers at these institutes,which differ from ordinary universities by thefact that there are relatively few, but very wellknown, permanent members, and most otherscientists are visitors from all around the world.We were very happy that we were both selectedfor this fellowship, as this enabled us to continueliving together while developing our careers,which is not at all trivial but was extremely important to us.We started our EPDI itinerary in 2009 by staying one year at the Max-Planck-Institute forMathematics (MPIM) in Bonn, located at theheart of this pleasant city on the river Rhine. InBonn there is a lot of mathematical activity, bothat the MPIM itself in the form of weekly seminarsand various workshops as well as at the Universityof Bonn and the Hausdorff Institute.Bonn is also well known as the city of Beethovenand indeed there are many classical music eventsaround the year, from Schloss concerts in thesummer to piano competitions and conducting

2011 events“The Unravelers Tour in France”26 September - 6 October: École Normale Supérieure Lyon

7 - 8 October: CIRM, Luminy

10 - 21 October: Université de Montpellier

31 October - 11 November: Université de Strasbourg

14 - 30 November: Université 1, Nancy

1st December 2011 - 6 April 2012: Nord-Pas de Calais region

Dates to be set for Rennes, Orléans and Grenoble.

Details of this event can be found on the Institute’s website.

“The Unravelers Tour in China”June : Alliance Française in Chongqing

July : Alliance Française in Macao

August - September : Alliance Française in Tianjin

From 7 to 9 September, IHÉSJoint master opening for students of Hadamard

Foundation founding institutions.

12 September, IHÉSAfternoon on Arithmetical Geometry on the occasion

of Takeshi Saito’s 50th birthday.

From 17 to 21 October, IHÉSDifferential Equations and Galois Theory Conference

as part of the celebration marking Evariste Galois’s

bicentennial, co-organised by Y. André, A. Buium,

P. Cartier, J.-P. Ramis and H. Umemura .

17 November, IHÉSCelebration of Chern Shiing-Shen’s centenary.

October, November 2011 - January, February 2012on Thursdays, IHÉSArithmetics and Algebraic Geometry Course,

organised by A. Abbes, C. Breuil and L. Lafforgue.

July 2012 (dates to be confirmed), IHÉSFrench-Asian Summer School

The European Post-Doctoral Institute forMathematical Sciences (EPDI), formed of teninstitutes spread throughout Europe, existssince 1995 to encourage the mobility of youngscientists at the European level.Testimony collected in March 2011.

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For more information: www.ihes.fr