August 19, 2010 THE FIELDS MEDALISTS

Elon Lindenstrauss Ngô Bảo Châu Stanislav Smirnov Cédric Villani Citation: “For the proof of con- Citation: “For his proofs of Citation: “For his results on Citation: “For his proof of the formal invari- n o n l i n e a r m e a s u r e Fundamental ance of L a n d a u rigidity in er- Lemma in percolation damping and godic theory, the theory of and the pla- convergence and their ap- automorphic nar Ising to equilibrium plications to f o r m s model in sta- for the Boltz- number the- through the t i s t i c a l mann equa- ory.” introduction physics.” tion.” Lindenstrauss has made far- of new algebro-geometric reaching advances in ergodic methods.” theory, the study of measure It was predicted in the 1990s, One of the fundamental and and used in many studies, that initially very controversial the- preserving transformations. His In the 1960's and 70's Robert the scaling limit of various two ories of classical physics is work on a conjecture of Langlands formulated various dimensional models in statisti- Boltzmann's kinetic theory of Furstenberg and Margulis con- basic unifying principles and cal physics has an unexpected gases. Instead of tracking the cerning the measure rigidity of conjectures relating automor- symmetry, namely it is confor- individual motion of billions of higher rank diagonal actions in phic forms on different groups, mally invariant. Smirnov was individual atoms it studies the homogeneous spaces has led Galois representations and L- the first to prove this rigorously evolution of the probability that to striking applications. Specifi- functions. These led to what for two important cases: perco- a particle occupies a certain cally, jointly with Einsiedler and today is referred to as the lation on the triangular lattice position and has a certain ve- Katok, he established the con- Langlands programme. The and the planar Ising model. The locity. The equilibrium proba- jecture under a further hypoth- main tool in establishing some proof is elegant and it is based bility distributions are well esis of positive entropy. It has cases of these conjectures is on extremely insightful combi- known for more than a hun- impressive applications to the the trace formula and in apply- natorial arguments. Smirnov's dred years, but to understand classical Littlewood Conjecture ing it for the above purposes a work gave the solid foundation whether and how fast conver- in the theory of diophantine ap- central difficulty intervenes: to for important methods in statis- gence to equilibrium occurs proximation. Developing these establish some natural identi- tical physics like Cardy's For- has been very difficult. Villani as well other powerful ergodic ties in harmonic analysis on mula, and provided an (in collaboration with Desvil- theoretic and arithmetical local groups as well as ones all-important missing step in the lettes) obtained the first result ideas, Lindenstrauss resolved connected to arithmetic geo- theory of Schramm-Loewner on the convergence rate for the arithmetic quantum unique metric objects. This problem Evolution in the scaling limit of initial data not close to equilib- ergodicity conjecture of Rud- became known as the Funda- various processes. rium. Later in joint work with nick and Sarnak in the theory of mental Lemma. After many his student Mouhut he rigor- modular forms. His work is ex- advances by a number of re- Professor, University of ously established the so-called ceptionally deep and its impact searchers in 2004, Laumon Geneva. Born in 1970 in St. Pe- non-linear Landau damping for goes far beyond ergodic theory. and Ngô established the Fun- tersburg, Russia. He studied the kinetic equations of damental Lemma for a special mathematical analysis with Vik- plasma physics, settling a Professor, Hebrew University, family of groups, and recently tor Havin at St. Petersburg long-standing debate. He has 2008- , Professor, Princeton Ngô established the Lemma in University, USA (2004-2010); State University. After graduat- been one of the pioneers in general. Born in Jerusalem, 1970. B. Sc ing in 1992 he moved to the the applications of optimal (Mathematics and Physics), Caltech where he received his transport theory to geometric Ngô's brilliant proof of this im- The Hebrew University, Ph. D. in 1996 under Nikolai and functional inequalities. He portant long standing conjec- Jerusalem, 1991; M. Sc. Math- Makarov. After short stints at wrote a very timely and accu- ematics, The Hebrew Univer- ture is based in part on the the Institute of Advanced Study, rate book on mass transport. sity, 1995; Ph.D. in introduction of novel geometric Mathematics, The Hebrew Uni- objects and techniques into Princeton and the MPIM, Bonn, versity, 1999. this sophisticated analysis. His Smirnov spent an important Born in 1973 in France. After achievement, which lies at the part of his career in Stockholm, studying mathematics at École Awards: The Anna and Lajos crossroads between algebraic where he came in 1998. Be- Normale Supérieure in Paris Erds Prize in Mathematics geometry, group theory and came professor at the Royal In- (1992-96), he became assis- 2009; Michael Bruno Memorial automorphic forms, is leading stitute of Technology and tant professor there. He re- Award (given by the Rothschild to many striking advances in researcher at the Swedish ceived his PhD in 1998. In “Yad Hanadiv” Foundation) Royal Academy of Sciences in 2000 he became a full profes- 2008; European Mathematical the Langlands programme as 2001. sor at École Normale Society Prize 2004; Salem well as subjects linked with it. Prize 2003; Clay Mathematical Awards: St. Petersburg Mathe- Supérieure de Lyon. In 2009 Institute Long Term Prize Fel- Professor,the Faculté des Sci- matical Society Prize (1997), he was appointed director of low 2003-2005; Leonard M. ences at Orsay. Born 1972 in Clay Research Award (2001), the Institut Henri Poincaré in and Eleanor B. Blumenthal Hanoi. After secondary school, Gran Gustafsson Research Paris, and part-time visitor of Award for the Advancement of he moved to France. He did Prize (2001), Rollo Davidson the Institut des Hautes Études Research in Pure Mathematics his PhD in Orsay under the su- Prize (2002), EMS Prize Scientifiques. 2001. pervision of Gérard Laumon. (2004).

REFLEXIONS August 19, Thursday

The Rolf Nevanlinna Prize The Gauss Prize The Chern Medal Award

Citation: “For smoothed analysis of Linear Citation: “For fundamental contributions to Citation: “For his role in the formulation of Programming, algo- number theory, oper- the modern theory of rithms for graph- ator theory and har- non-linear elliptic based codes and monic analysis, and partial differential applications of graph his pivotal role in the equations and for theory to Numerical development of mentoring numerous Computing.” wavelets and mul- students and post- tiresolution analysis”. docs in this area”. Linear Programming is one of the most Meyer has made Nirenberg is one of useful tools in ap- fundamental contri- the outstanding ana- plied mathematics. The oldest algorithm bution to a number of mathematical areas. lysts and geometers of the 20th Century for Linear Programming, the Simplex Around 1970, he developed the theory of and his work has had a major influence in Method, works very well in practice, but model sets in number theory, which has the development of several areas of math- mathematicians have been perplexed become an important tool in the mathemat- ematics and their applications. He has about this efficacy and have tried for long ical study of quasicrystals -- space-filling made fundamental contributions to the un- to establish this as a mathematical theo- structures that are ordered but lack trans- derstanding of linear and non-linear partial rem. Spielman and his co-author Shenhua lational symmetry -- and aperiodic order in differential equations (PDEs) and related Teng developed a beautiful method and general. Together with Ronald Coifman aspects of complex analysis and geometry, proved that, while there may be patholog- and Alan MacIntosh he proved the continu- the basic mathematical tools of modern sci- ical examples where the method fails, ity of the Cauchy integral operator on all ence. He developed intricate connections slight modifications of any pathological ex- Lipschitz curves, a long-standing problem between analysis and differential geometry ample yields a “smooth” problem on which in analysis. and applied them to the theory of fluid flow the Simplex method works very well. and other physical phenomena. Meyer played a leading role in the modern A second major contribution of Spielman development of wavelet theory, which has Nirenberg’s name is associated with sev- is in the area of coding. Much of the pres- had a spectacular impact in information eral major developments in analysis in the ent-day communication uses coding, ei- sciences, statistics and technology. Fourier last 65 years. His theorem with August ther for preserving secrecy or for ensuring analysis is a universal tool in applied math- Newlander on the existence of almost com- error correction. An important technique to ematics, and due in a large measure to plex structures has become a classic. One make both coding and decoding efficient Meyer’s work, wavelet theory has become of the most widely quoted results in analy- is based on extremely well-connected the new name for Fourier analysis. He con- sis is that a priori estimates for general lin- graphs called expanders. Spielman and structed the first non-trivial wavelet bases ear elliptic systems, which he obtained with his co-authors have done foundational and wavepackets that dramatically ex- Shmuel Agmon and Avron Douglis. His fun- work on such codes and have designed tended the expressing power of wavelets. damental work with Fritz John on functions very efficient methods for coding and de- This led to many applications in practice – of bounded mean oscillation was crucial for coding. These codes provide an efficient in image processing, data compression, later work of Charles Fefferman on the solution to problems such as packet-loss statistical data analysis and elsewhere. space of such functions. In collaboration over the internet and are particularly useful Among the many applications of Meyer’s with Joseph Kohn, he introduced the nation in multicast communications. They also work, the techniques for restoring satellite of pseudo-differential operator, which has provide one of the best known coding images and the image compression stan- been influential in many areas of mathe- techniques for minimizing power con- dard JPEG-2000 deserve particular men- matics. Other significant works of Niren- sumption required to achieve reliable com- tion. berg, which he has carried out in munication in the presence of white collaboration with others, have been on Gaussian noise. More recently, he has found a surprising solvability of PDEs, existence of smooth so- connection between his early work on the lutions of a class of PDEs and equations of Professor, Yale University. Born in model sets used to construct quasicrystals fluid motion of Navier-Stokes kind. He has Philadelphia in March 1970. B.A. in math- -- the ‘Meyer Sets’ -- and ‘compressed published over 185 papers and has had 46 ematics and Computer Science from Yale sensing’, a technique used for acquiring students. (1992), and Ph. D. in Applied Mathematics and reconstructing a signal utilizing the from M. I. T. (1995). His thesis was on prior knowledge that it is sparse or com- Emeritus Professor, Courant Institute of ‘Computationally Efficient Error-correcting pressible. Based on this he has developed Mathematical Sciences, New York Univer- Codes and Holographic Proofs’. He spent a new algorithm for image processing. A sity. Born February 25, 1925, in Hamilton, a year as a National Science Foundation version of such an algorithm has been in- Ontario, Canada. After receiving his bach- (NSF) post-at University of California, stalled in the space mission Herschel of the elor’s from McGill University in 1945, he Berkeley, and then taught at the Applied European Space Agency (ESA). went to NYU from where he obtained his M. Mathematics Department of MIT until S. (1947) and Ph. D (1949), under the di- 2005. Professor Emeritus at École Normale rection of James Stoker. Nirenberg then Supérieure de Cachan, France, Born on joined the faculty of NYU. He was one of Awards: Fulkerson Prize, jointly awarded July 19, 1939. He graduated from École the original members of the CIMS. He by the American Mathematical Society Normale Supérieure, Paris, in 1960 and spent his entire academic career at Couran (AMS) and the Mathematical Program- became a high school teacher until 1963. from where he retired in 1999. ming Society (2009); the Gödel Prize, He then obtained Ph. D. from Université de jointly awarded by the Association for Strasbourg in 1966. He was his own thesis Awards: American Mathematical Society’s Computing Machinery (ACM) and the Eu- supervisor. He has been a professor at Bôcher Prize in 1959 for his work on PDEs, ropean Association for Theoretical Com- École Polytechnique, Université Paris- Jeffrey-Williams Prize of the Canadian puter Science (EATCS) for the paper with Dauphine and has also held a full research Mathematical Society in 1987 and the Teng on ‘Smoothed analysis of algorithms: position at Centre National de la Steele Prize of the AMS in 1994 for Lifetime Why the simplex algorithm usually takes Recherche Scientifique (CNRS). France, Achievement. He was the first recipient in polynomial time’. He served as a professor at École Normale mathematics of the Crafoord Prize, estab- Supérieure de Cachanduring 1999-2009. lished by the Royal Swedish Academy of Spielman has applied for five patents for He is a foreign honorary member of the Sciences, in 1982. In 1995 he received the error-correcting codes that he has in- AAAS. He has also been awarded a Doc- National Medal of Science, the highest ho- vented and four of them have already torate (Honoris causa) by Universidad Au- nour in the U. S. for contributions to sci- been granted by the U. S. Patent Office. tonoma de Madrid. ence.

REFLEXIONS August 19, Thursday Abel Prize: The Norwegian Nobel Prize for Maths The prize is administered by the Norwegian Academy of Science and Letters !"#!$%$&'$()*$( will vary according to returns nor, met Arild Stubhaug, who from the corpus fund, it will be had written Abel's biography just he Abel Prize is an interna- similar to the amount of a Nobel the year before. Hermansen Ttional prize established in Prize, the most coveted prize in briefed the Norwegian Ministry 2001 and awarded for outstand- the sciences, which, however, of Education, Research and ing lifetime achievements in does not include mathematics. Church Affairs about the idea mathematics. The prize is The Fields Medal of the IMU, and Stubhaug made the pro- named in honour of the great which was given for the first posal to the Department of Norwegian mathematical genius time in 1936, is generally re- Mathematics, University of Oslo. Niels Henrik Abel (1802-1829) garded as the `Mathematician's The university took up who died at the young age of Nobel' and is extremely presti- the matter seriously and set up 26. Abel is often compared with gious. But only mathematicians a working group comprising the Indian mathematical wizard below the age of 40 are eligible Professors Jens Erik Fenstad, Srinivasa Ramanujan. for the Fields Medal and it does Arnfinn Laudal, Ragni Piene, The prize is administered not have any monetary prize ex- Yngvar Reichelt and Nils Voje by the Norwegian Academy of cept for a symbolic amount. The Niels Henrik Abel Johansen, and the author Stub- Science and Letters and the Abel Prize, on the other hand, haug. The working group sub- winning candidate is selected has no such restriction and is inspired by the knowledge that mitted the proposal to the on the basis of the recommen- comparable to the Nobel Prize Alfred Nobel's plans for annual Norwegian Prime Minister in dation of an international com- both in terms of value and the prizes, made known in 1897 it- May 2001. "Norway is a small mittee chaired by a Norwegian. eligibility criterion. self, would not include mathe- country. There are close con- The committee consists of five The Prize was estab- matics. Although the support to nections and people who matter outstanding mathematicians ap- lished as part of the events Lie's suggestion from leading generally know each other. So pointed by the Academy upon leading up to the celebrations of mathematics centres in Europe we could lobby with the govern- recommendations by the Euro- Abel's 200th birth anniversary, a was enormous, the contacts ment and after some time we pean Mathematical Society, the little over 100 years after the and promises were apparently were very surprised to learn that International Mathematical idea was mooted in 1899 by the tied too much to Lie personally the government had agreed to Union (IMU) and the Academy's famous 19th century Norwegian and hence it could not be re- fund this prize," says Piene. group for pure and applied mathematician Sophus Lie alised easily. On August 23, 2001, dur- mathematics. There are three (1842-1899) shortly before his During Abel's first cente- ing a speech at the University of IMU nominees and one each death. nary celebration, King Oscar II Oslo, Prime Minister Jens Stil- nominated by the other two bod- In 1902, as the celebra- of Norway got interested in the tenberg announced his govern- ies in the committee. tion of Abel's first centenary ap- idea and revived the proposal in ment's decision to establish the The current value of the proached, three main tasks had close association with the Sci- Abel Fund. Though the prize prize is NOK 6 million (approxi- been specified: to arrange a ence Society of Christiania, now has gained stature and prestige, mately $980,000), which is de- broad cultural commemoration the Norwegian Academy of Sci- no one thinks that it will replace rived from the annual returns on of Abel, to raise a worthy monu- ence and Letters, and Norwe- the Fields Medal. "This is a dif- the NOK-200-million Abel Me- ment in his memory and to es- gian mathematicians Carl ferent kind of prize and it is not morial Fund established by the tablish an international Abel Stormer and Ludvig Sylow. meant to compete with the Norwegian government in 2001. Prize. Though Lie had been the However, with the dissolution of Fields Medal," points out Piene. That is, while the fund belongs first enthusiastic proponent of the union between Sweden and "In fact, the IMU helped us in to the state, proceeds from it are establishing an Abel Prize, the Norway in 1905, the plans were establishing the prize and its used by the Academy. The first idea died with him. Lie's sug- once again dropped. It was re- backing was useful in our lobby- Abel Prize was awarded in gestion for an Abel award every vived only in August 2000 when ing within Norway, which was 2003. five years for outstanding work an industrialist, Tormod Her- very important," she adds. Though the prize money in pure mathematics had been mansen, the then CEO of Tel- (From Frontline, April 20, 2007) Why there`s no Nobel Prize in Maths? !"!$%$&'$()*$( Both the apocryphal stories were debunked myth with juicy bits thrown in. in an article by mathematicians Lars Gård- "The true answer," say Gårding and Hor- ne of the oft-cited reasons for Alfred ing and Lars Hormander in the journal mander, "is that, for natural reasons, the ONobel not instituting an award for Mathemetics Intelligencer in 1985. Accord- thought of a prize in mathematics never en- mathematics is that the famous Swedish ing to them, Mittag-Leffler and Nobel had al- tered Nobel's mind." Nobel's final will be- mathematician Gösta Miagnus Mittag-Lef- most no relation to each other. Nobel queathed $9 million for a foundation whose fler had run off with Nobel's wife. Though migrated to Paris in 1865, when Mittag-Lef- income would support five annual prizes in there is no evidence to support this story - fler was still a student, and rarely returned fields which, except for medicine, were because Nobel never married - it has as- to visit Sweden. There is no evidence of any close to Nobel's interests. Economics was sumed a life of its own. One comes across animosity between them either. In fact, dur- added in 1969. He perhaps simply did not different versions of this: that the woman ing Nobel's last years Mittag-Leffler is care much for mathematics because it was was not Nobel's wife but the one he had known to have been engaged in persuading not considered a practical science, which proposed to or that she was his mistress Nobel to designate a substantial part of his could benefit humanity (a chief purpose of and so on. fortune to Stockholm Hogskola (which later creating the Nobel Foundation). His will Another story is that Mittag-Leffler, in the became Stockholm Universitet). speaks of prizes for those "inventions or process of accumulating considerable Apparently, Nobel had originally intended to discoveries" of greatest practical benefit to wealth, had antagonised Nobel. Nobel, do this but eventually formed the Founda- mankind. afraid that Mittag-Leffler might win the prize tion much to the disappointment of As Peter Ross points out in Math Horizons for mathematics, did not institute a prize for Hogskola. Following this, academic rivals of (1985), "with the blossoming of computer mathematics. This also seems far-fetched Mittag-Leffler at Hogskola alleged that it science, statistics and applied mathematics as there were greater mathematicians such was Nobel's dislike for Mittag-Leffler that in addition to mathematics itself, a strong as Henri Poincaré and David Hilbert around made him change his mind. This incident case could be made for a new Nobel Prize at that time. could have contributed to the prevalent in the mathematical sciences".

REFLEXIONS August 19, Thursday Mathamatics is a fashionable subject, says Lászlό Lovász

Lászlό Lovász, President of the three offers which are all very solutely open. He liked to sit in a International Mathematical Union generous. Whichever is decided, room with people and chat with (IMU), is the Fields Medal Prize I am sure, will give a good stable them and raise problems. In par- Committee Chair for ICM 2010. permanent location, secretarial ticular he liked if there were He was the recipient of the Na- help, internet connection: To- young people, high school kids tional Order of Merit of Hungary morrow at the General Assem- there. They were new subjects, in 1998. In 1999, he was bly, we’ll approve the whole thing but some of the problems that he awarded the Knuth Prize, and then decide which of the raised were actually accessible Göedel Prize came in 2001 and three bidders will get the office. without a lot of background the Wolf Foundation Prize in knowledge. That’s how many of mathematics for outstanding :6';898859$6345"945 these young people got inter- contributions to combinatorics, 2)89?975(9&6'9(804(8(926 ested in this field. Lászlό Lovász theoretical computer science %689709269 '5"73&945 And he was travelling:he had and combinatorial optimization. @BC9 )729 45!'8508( some arrangement that he could matician should know about be- Lovász has obtained ground &6'39(8041465# travel around the world and cause they influence the way we breaking results in discrete come back to Hungary, because think about mathematics. It was mathematics which have had We (me and wife) always con- Hungary was behind the Iron a very exciting time because very significant applications in sidered it to be somewhat tem- Curtain. I wouldn’t say it was im- combinatorial mathematics and other areas of pure and applied porar. We liked it very much possible to travel but how much computer science grew side by mathematics as well as to theo- there, but somehow we decided travel you could do was limited. side and it was almost impossi- retical computer science. He that when we are getting close to And he always had the newest ble to separate them. solved several outstanding prob- retirement we want to go back to information. lems including the perfect graph our home country. We thought 192)838979!70'5794592)8 conjecture, Kneser’s conjecture that we should give a few years )69$719&6'39451437 2870)45"975(9!873545"96 and the determination of the to re-integrate before we retire. If 2465# 10)66!9 %72)8%72401 Shannon capacity of the penta- you just retire and go back, you 56$7(7&19 06%738(9 26 gon. may not have the connection. When I was fourteen, I was &6'3910)66!9(7&1# He shares his experiences in Another element of the decision looking for a high school to go to. conversation with B.Sury. was that our son turned fourteen That’s when this class for math- If you ask about it in Hungary, I when we moved back. He was ematically talented kids was would say that the situation has 6$9$719&6'39283%971 very good in math and there is a formed. My teacher recom- changed with respect to mathe- ,3814(8529692)893# special school in Budapest for mended me to go to this class, matics because in those days, mathematically talented kids. which was fantastic. I consider it mathematics was considered to It was a busy time. We had to Both my wife and I went to this the best move in my life. An ex- be ‘the’ subject to study because there were no political sides. So prepare ourselves for some diffi- school . So we thought it would cellent school with excellent you didn’t have to put up with all cult decisions. Most prominent of be good for him to go to that other kids and very good teach- sorts of political pressures if you these is the establishment of a school. And that worked out in ers  I really liked it. After that, it wanted to do mathematics. It permanent office for the IMU. the end and he enjoyed the was sort of automatic. was international. A mathemati- That was a big step which we school and got excellent prepa- cal result is recognized in the had to work out carefully so that ration for his mathematical stud- 719 06%'2839 1048508 same way all over the world but the financial and other problems ies at the university. )8!8(9&6'9459&6'39073883 if you do say, archaeology then are solved. On the other hand, I 71979%72)8%7240475# clearly Hungarian archaeology think that the Executive Commit- 6$9(4(9 '5"73&906%8 has limited interest. Some inter- tee was very active and helpful 269)7891'0)97912365"9237 I was always interested in com- est outside, but it is limited. And and we had a very good working (42465945906%457263401# puters. Hungary didn’t have a lot also, mathematics didn’t need a relationship between ourselves. of computing power in those lot of expensive equipment like I think in this particular field, days. Computers were very rare physics. So mathematics was a 8389 2)8389 75&9 %7763 mainly combinatorial graph the- when I was a university student. very fashionable subject. (804146519 $)40)9 $838 ory which is a branch of combi- But we got interested in algo- Then the political situation 27859 459 2)8189 6'3 natorics  just one or two rithms at least on a theoretical changed, democracy came, cap- &8731# Hungarian mathematicians level. So at least theoretical com- italism was re-established. So The permanent office was such started to work on it back before puter science started, which ac- many young people want to go a decision. We realized that we World War II, even before World tually is quite closely related to into finances, banks, stock mar- don’t have the finances to rent War I actually. Then they had graph theory; in many points, it kets and these sort of things. an office and hire staff. IMU students and some of the stu- has connections. In a sense, There is a decrease in interest doesn’t have much money and dents were absolutely outstand- graph theory may be one of the which is all over the world, you membership fees is small. So, ing people. König was the most important mathematical can feel it all over the world. I what we decided is to ask the Founding Father of this school backgrounds of computer sci- don’t know how it is in India but community for help. We an- and he wrote the first text book ence just like say, mathematical in Hungary and in the West, it is nounced that institutions can bid in the world on graph theory. analysis is the background for unfortunate because somehow for the hosting of our office. The Paul Erdös was one of his stu- physics. there is this feeling that, you idea was that for a big research dents. He is very well known and Computer science was begin- don’t have to put up with all institute to spare a room and there are books written about ning to grow in the late sixties, those really hard studies that you maybe some secretarial help him. He is one of the most influ- seventies. It became a separate have to do if you do a hard sci- would not be such a big deal. ential mathematicians in the subject. It was recognized that ence. And we got a fantastic reply and twentieth century. Through his there are mathematically very in- generous offers. We started off work many people became inter- teresting and in fact basic prob- with eleven or twelve offers and ested because the way he did lems in computer science which ...Continued on Pg 8 now we are down to the best mathematics was always ab- in a sense, I think every mathe-

REFLEXIONS August 19, Thursday Princeton Woman Professor Makes Waves !""#$%&'%()*+,&#, making wavelets methods a practical basic tool of applied mathematics’. ngrid Daubechies, whose birthday was Iyesterday, is the first woman President In September 2006, the Pioneer Prize from (2011–14) of the International Mathematical the International Council for Industrial and Union (IMU). She is also among the first four Applied Mathematics was awarded jointly to women to be plenary speakers at the Inter- Ingrid Daubechies and Heinz Engl. The cita- national Congress of Mathematicians tion for Daubechies read: ‘...Daubechies’ (ICMs). Emmy Noether gave a plenary lec- best known achievement is her construction ture at the 1932 ICM in Zurich, Karen Uhlen- of compactly supported wavelets in the late beck at the 1990 ICM in Kyoto, and Ingrid 1980s. Since that time she has advanced the Daubechies and Marina Ratner at the 1994 development of biorthogonal wavelet bases. ICM in Zurich. !"#$%&'()*+,-$+. These bases are currently the most com- monly used bases for data compression. Daubechies was born in 1954 in Belgium physicist, winning several awards such as Daubechies’ name is widely associated with and is now settled in the US (from 1987) the Louis Empain Prize for Physics (1984), the biorthogonal CDF wavelet. after her marriage to Robert Calderbank, the Leroy P. Steele prize for exposition also a mathematician. She has been a Fel- (1994) for her book Ten Lectures on Wavelets from this family are cur- low of the MacArthur Foundation from 1992– Wavelets, the American Mathematical Soci- rently used in JPEG 2000 for both lossless 1997. She is the first woman Professor of ety Ruth Lyttle Satter Prize (1997), and the and lossy compression. Her continuing Mathematics at Princeton University, New wavelet research also resulted in path- IEEE Information Theory Society Golden Ju- Jersey – she works in the Department of breaking work including the discovery of Wil bilee Award for Technological Innovation Mathematics and in the Program in Applied son bases. This discovery led to the exis- (1998). and Computational Mathematics there. Her tence of cosine packet libraries of orthonor- research interests include time–frequency mal bases and Gaussian bases. These are She is the first woman to receive the Na- analysis (especially wavelets) and its appli- now standard tools in time frequency analy- tional Academy of Sciences Medal in Math- cations in mathematics and other sciences, sis and numerical solutions of partial differ- ematics (2000) – the award honoured her engineering and art. ential equations.’ ‘for fundamental discoveries on wavelets and wavelet expansions and for her role Daubechies is a mathematician and a Daubechies (Yes She Is!) The New IMU President !"#$%!#&$'()$($*!+$!, how I find the problems that I combine that with probability. math than what you usually see. +'-!#-+./(*$ /!0+-0+ work on – by curious listening. Every branch of mathematics So, bringing in these baby appli- (01$ (*)!$ /!0/#-+-$ (22*.3 can be applied and applied cations is not necessarily a good /(+.!0)4$5!$%'(+$1!$6!" 5'-$(22*./(+.!0)$!,$9(+'3 mathematicians actually need to way. They have to be there too, (++#.7"+-$ +'.)$ (/'.-8-3 -9(+./)$ (#-$ 0!+$ %.1-*6 know as much pure mathematics but mathematics is more about 9-0+: &0!%0444 as they can. When you work in finding ways to think about a applied math, the problem de- problem and of solving. Mainly to curiosity... As long as They are and they aren’t. All cides what mathematics you I can remember, I’ve been inter- the engineers who work with need to learn. I am an applied I was on leave in Belgium the ested in understanding how mathematics, of course, know – harmonic analyst, but I am now first six months of this year and I things work. I am also interested they use mathematics. What is working on this problem where I became very involved in setting in making connections – if I learn not as widely known, I think, is need more differential geometry up a framework for a contest. It’s something new and it reminds how things that develop in one and so, I have a post-doc teach going to be for high school stu- me of something else, I try to re- field can be really useful in an- me differential geometry and it’s dents this fall. We will pose math ally clarify this, I like to really un- other field. I was talking to great because as I said, what I problems but not math along the derstand and articulate this kind somebody here who used to really enjoy is learning new conventions of what they see in of hunch. At first such hunches work in ecology, plants and in- things. high school but nevertheless ac- are at the level of ``science fic- sects and their interactions and cessible to students from high tion”. relationships. And now she has ;/'!!*$/'.*1#-0$1!0<+$"03 school. They are not considered moved to a different institution 1-#)+(01$ 9(+'-9(+./)= easy but are not problems in You have to really work in order and works in models for cancer +'-$,!#9"*(-> which a lot of computation has to to make the link explicit, and research but the mathematics be done. They have to think. We then you disentangle it and you she is doing are the same. I don’t know about India. But in are going to challenge classes to find structure. You find ways of Europe and America, too much think about them together. connecting things that might not So, on the one hand, you can of mathematics in high school seem connected before or lead- have the same mathematics that has become formulae, very di- We are hoping to attract a lot ing to a very important applica- you use in quite different applica- vorced from other things in sci- of attention from school children tion. This is something that I like tions. On the other hand, you ence or applications or when and we are hoping to show them to do. also have applications that re- applications are brought in, they that it isn’t that the math that they quire a completely different feel very artificial. They use see in high school is not math, At present, I’m involved in col- branch of mathematics. words of an application in eco- but it is a very technical kind of laborations with people in differ- nomics or so but in practice, it math that may be a good prepa- ent branches – in biology, in I am involved in an application still seems very far from the ration for calculus and engineer- psychology and recently even in in biology where we extensively problems that people have in ing and sciences but there is so art history – mainly because I re- use differential geometry. Data their lives. much more to mathematics than ally like to listen and learn from analysis is becoming increas- that. Plus, there may be students people who are experts in what ingly complex and people are re- ?!$6!"$'(8-$(06$)"@@-)3 who don’t like that technical as- they do. I enjoy learning more alizing that more than just using +.!0)$,!#$.92#!8-9-0+: pect but who would be great and then I like to think about the probability and linear algebra, mathematicians. problems they have or connec- they need to bring in topology When you want to do serious tions that could be made. That’s and differential geometry and applications, you need more ...Continued on Pg 7

REFLEXIONS August 19, Thursday Korea Wins The Bid For ICM 2014 Geethanjali Monto also. But we felt that we need to matics in Korea and also in the go forward and really get in- developing world are happening. volved in the core of mathemati- Hopefully the traditionally pas- cal research. We wanted to sive member countries of IMU encourage our young re- may get more involved in IMU searchers in the positive direc- activities, so that more balance tion and so for that we needed in terms of distributing resources more mathematics jobs, aca- and mathematical research geo- demic jobs, more post doctoral graphically or area-wise will positions and research grants occur by this Korean ICM.’ and mathematics. For that we needed something that can act In his presentation at the Gen- as a pivot and we thought that eral Assembly, Hyungju Park de- this ICM in Korea would do that. scribed the ‘story of Korea’ in Our motto or keyword for this ef- terms of its economy, education, fort was ‘dreams and hopes for culture, accessibility and history late starters’ meaning Korea was of mathematics. ‘In 2008, Korea he next International Con- local mathematical community, a late starter. However we think ranked eleventh in SCIE publica- Tgress of Mathematicians good financial provisions and we made such rapid progress in tions in math, almost tripling its (ICM 2014) will be hosted by convenient congress centres. a short span of time and came to publications in 10 yearsGIn IMO Korea. This decision was taken The Executive Committee de- where we are, and if we have the (International Mathematical by voting at the 16th General As- cided to recommend Seoul as ICM, maybe we can inspire Olympiad), Korea is now steadily sembly (GA) meeting held in the site for the next ICM 2014. those developing countries that ranking third or fourth...Math is Bangalore, India from 16–17 Au- Speaking to Hyungju Park, Chair are still in a difficult situation ex- becoming a very popular subject gust 2010. The GA usually of the Seoul ICM 2014 organiz- periencing lack of resources. So in Korea. When kids enter col- meets every four years at a ing committee and Professor and we thought we would put our em- lege, they take a college en- place and date which is in prox- Chair of the Department of Math- phasis on that. trance exam and they choose imity to that year’s ICM. The ematics, POSTECH just before their majors. The most popular 2010 ICM is to be held at Hyder- the announcement of the site for We wanted to prove our earnest area right now is medicine and abad from 19–27 August. ICM 2014, on their bid for the intention not just verballyGwe the second popular subject is The first ICM in 1897 established same: ‘Korean mathematical so- actually offered to provide 1000 mathematics in major universi- certain objectives of the Con- ciety decided to bid for ICM 2014 mathematicians from developing ties. This is something we didn’t gress, the first two of which in 2007. At the beginning of July world to attend the ICM if it is ap- expect before. So definitely math were: (1) To foster personal rela- in 2007, the Korean math society proved, so that those mathemati- is becoming a very popular sub- tions between mathematicians of formed a bidding committee for cians from the developing world ject and we think that our ICM ef- different countries; (2) To present ICM 2014 and I was the Chair of who may not have been able to forts contributed to that also. We in the lectures of the plenary ses- that bidding committee. The rea- experience ICM would be able to are telling young students that sions and the different sessions son we decided to make that ef- experience it and bring it to their math is a fascinating subject and an overview of the current state fort wasGKorea was a late home countries and inspire their there are things that are happen- of the different areas of mathe- starter in modern mathematical younger generations. It can ben- ing.’Regarding Government en- matical sciences and their appli- research. We started very late eficial. And the government was couragement for the 2014 ICM, cations, and to discuss specific and even until 1980’s, for exam- very enthusiastic in supporting Park said that 350,000 dollars problems of particular impor- ple in 1981, we had only 3 pa- us and has granted us budgets have been awarded to the bid- tance. pers that were published in for the bidding efforts and every- ding committee for its bidding ef- international mathematical jour- thing. After the IMU Executive forts most of which they spent in Since the first ICM held in 1897 nals from Korea. Committee recommended Seoul organizing national conferences, at Zürich, these Congresses and as a candidate city for the ICM, so that international scholars their General Assemblies have So Korea was in a very difficult the Korean government, for ex- could visit them in Korea and travelled all over the world from situation, had a lack of re- ample, increased research also that young Korean mathe- Paris (1900) – UK (1912) – sources, had a lack of mathe- grants for mathematics and they maticians could attend the na- Strasbourg (1920) – Oslo (1936) maticians and also a lack of have also established more re- tional meetings. This year, the – USA (1950) – Nice (1970) – students. Somehow, things search centres where young Government provided another Vancouver (1974) – Kyoto started to change from late 80s, post docs can get training. The 350,000 dollars most of which (1990) – Berlin (1998) – Beijing early 90s. Now for example in whole infrastructure in mathe- was used to aid large scale par- (2002) – Madrid (2006) – India terms of quantity, let’s say, in matics is being rapidly changed ticipation of Korean mathemati- (2010), to name some. 2008 when we look at the statis- because of the ICM. So we think cians in the 2010 Hyderabad tics, Korea ranked eleventh in a lot of good things for mathe- ICM. The ICM 2014 Site Committee the world in terms of number of comprising of Lászlό Lovász publications. So in this span of (IMU President), Zhi-Ming Ma 20–30 years, Korea made an al- (IMU Vice President), Martin most unprecedented progress in Grötschel (IMU Secretary) and mathematics, not just in quantity Manuel de Léon (Chair of previ- but quality. Now some high qual- ous ICM) visited the three candi- ity results are coming from dates or bidders namely Korea. In 2008, we had 2500 Montreal (Canada), Rio de mathematicians who are mem- Janeiro (Brazil) and Seoul bers of the Korean mathematical (South Korea). Manuel de Léon society. Of these 1100 or 1200 said that the Site Committee were professors in mathematics. found the three bids really good So the Korean mathematical From left to right : Hyang-Sook Lee, Jeong Han Kim, Hyungju Park with a strong involvement of the community has grown in size

REFLEXIONS August 19, Thursday Family No Hindrance For a Woman Mathematician ...Continued from Pg 5 comes out with great results – it ably well off or middle class. I like the idea of fostering men- ...We tend to teach math happens, but it is exceptional – They had time on their hands toring relationships that I heard by asking students for a suspen- people talk a lot to each other and if they were interested in mentioned at the IMU General sion of disbelief. ‘If you become and explain with their hands and math, then they would do math Assembly. For instance, in my an engineer, you will need this make sketches and so on. They problems. So there was a de- case, my children are now at uni- stuff! Don’t worry if you don't un- use a lot of metaphors, they mand for math problems in a versity in the United States. That derstand how this will be useful have hunches and they have to women's magazine. means that they are basically in- and so on. You just believe us, make it rigorous but it is a much dependent. Even in other coun- you’ll need it.’ I don’t know if more intuitive and social field To have a career path in math tries, children become that’s a very good way to teach. than people realize. I think we for women, you have to have a independent after university. At Now I happened to enjoy math a should convey that much more. society where a career is possi- some point in your life, you still lot even in such courses be- ble at the same time as having a have plenty of energy and you cause I was good at it and I was 8+'" %&'+'" $/1" !6')($* family, because most young actually have more money than good at playing with these )&$**'/9'!"0$)(/9":.#'/ women want to have a family. when you were young. And things. But I think I would have 6+.0'!!(./$*!;" '!6')($**1 Well, most young men too, but many of us are idealistic and enjoyed a different type of math (/"-'<'*.6(/9").5/%+('!7 for young men – if the society is would like to help. So CDC course even more. So with this such that if they have a wife who (Commission for Developing contest, we want to try to get kids The important thing is to make takes care of the children, then Countries) could be an organiza- to see that mathematics is more sure that the profession gets set of course, they can have a ca- tion that identifies interesting op- than only what the textbooks in up in such a way that it is possi- reer. But if women don’t have the portunities where people who high school contain. ble to combine having a family. In possibility of a framework in want to take part of a sabbatical many cultures, women are still which they can have a family and to help could then contribute !" #$%&'#$%()$*" +', the most important care-givers to a career that involves their brain some of their own resources but !'$+)&"-./'"-(00'+'/%*1"(/ young children. It’s perfectly then8There are too few women for an already well-identified tar- %&'"23"$/-"45+.6'7 compatible with being a mathe- in mathematics now. If we get get. And not just to go and give matician. There’s no problem in more women, it will be more ob- lectures for a week or so – that The structure of how people get having to think about mathemat- vious to young smart women that doesn’t achieve anything – but to into their careers is different. In ics and take care of children. It is it is possible. go for a longer visit, build men- the States, you have graduate toring relationships that can be programmes. You apply to a sustained. So I think a lot is pos- graduate programme without sible and we could, within one having identified an advisor with generation, see a big difference whom you intend to work. Once there, and make a big difference. you are in the programme, you try to find a match with an advi- A&'+'"-."1.5"!''"#$%&, sor. In Europe, the funding is '#$%()!" &'$-(/9" (/" %&' done in such a way that you 05%5+'7 have to have a match with an ad- visor even before you start. So In mathematics, developments you find an advisor, the advisor come from people making con- may have money and so you nections between sub-fields in make that match. I regret that a mathematics. If you look, for in- bit because on the one hand, it stance, at Fields medals in past means that you are really mar- years – very often, they come ried to that advisor form the start. from connections that didn’t exist It also means that you are much and had not been established. less involved in a programme But I also see new applications where there are a lot of different Ingrid Daubechies requiring structures that people interests and money and people who build the applications grope and different branches of mathe- a problem if the whole responsi- 8!"%&'"/'=%" >2"?+'!(, for and try to build, but that re- matics. bility for minding the children 24 -'/%;"&.:"-."1.5"6*$/"%. quire a better setting and that will hours out of 24 comes on the #$/$9'"$**"%&'!'"/':"+', lead to new fields and construc- In a good graduate programme shoulders of one person. Then !6./!(@(*(%('!7 tions within pure mathematics. in the States, you have students you cannot be anything else. If And I see both of them happen- talking to each other who are in- there is a structure in the society When I am new President, I will ing. terested in number theory or where it is very well possible to have some relief from my duties analysis or yet other topics. Peo- be a mother but also have time at Duke. I negotiated that when I The most spectacular things will ple may still decide what field for other pursuits, then there’s no knew that this was a possibility. I come from applications; there they are going to go in. That, I problem. think it will be very interesting. I will be plenty of things that will like better in the States. On the am very interested in how come from biology, for instance. other hand, becoming a mathe- Through child care or through emerging countries develop But the interesting ones are not matician and the way you do re- extended family8there are mathematics. There is enormous the ones that I can describe to search is the same everywhere many ways in which this can be potential in young people and you now. They are the ones that –you think about problems, you solved. Once that is possible, they are interested. In a sense, will grow out of applications be- learn about what’s going on and then women can think about mathematics is easier for an cause we need them. And thirty you try to think about new ways mathematics. It’s actually very lit- emerging country to develop years from now, people will trace of doing things. tle known that in the nineteenth than physics or chemistry be- back to those first applications. If century, in Britain for instance, cause you need to have a big I could describe them now, they Research in mathematics is there was a magazine with math layout in materials and labs and would not be as interesting as I also a much more social thing problems for women, a Ladies lot more money. In mathematics, expect them to be. than many people realize. In the Almanac. This was, of course, once you build a nucleus of peo- exception where somebody sits for women who had some leisure ple who can work together, then in seclusion for many years and time, women who were reason- the sky’s the limit! Geethanjali Monto / REFLEXIONS August 19, Thursday Continued from Pg 4 ‘The Exciting Question in Applied Mathematics Today Is to Understand Complex Large Structures’ catch up easier than say an ex- recognizable at a rather early sides research. pensive biological research. It’s age. I have seen this in many So I think there’s truth in that a lot more difficult to provide fa- cases in young kids. There’s one but I don’t think it’s like with forty, cilities for that. There are some, who thinks in a different way; the you should retire and go to sail not too many, institutions in the others are just sleepy. If you are around the world. developing world which are on multiplying some numbers, they level with the best; Tata Institute ask ‘why are you doing it like C%&1&# 42# "2!# $%+/< for example, IMPA in Brazil, Ts- that?’ That means that these stu- )($%&)($+,-#+-#%&(4&4#+/ inghua University in China dents can start studying mathe- $%&#=!$!1&: which are really on level with the matics early. I am not in favour of That is always very difficult to world’s best institutions. And sending kids early to the univer- predict because mathematics hopefully there will be more. sity. I think it’s much better if has its internal logic which is There are other ambitious places there is some organization or driving it forward. There are  I hope they will be successful. some people who are giving some big developments which them some problems that sort of come entirely from the internal enriches what they learn but not need. There have always been Lászlό Lovász 62#"2!#$%+/<#(#)($%&* )($+,+(/# %(-# )21& necessarily by pushing it past such developments. It is also 02/.&3+$"#+/#812=&--+2/(0 through university. I know that in driven by applications. The one !"#$%&#'("#)($%&)($* 1&-&(1,%# $%(/# 2$%&1# -,+* the United States that’s the way thing I see is that the need of ap- +,-#+-#$(!.%$#+/#$%&#,0(--* &/$+-$-:# >%&"# -("# $%($ to do. That’s of course one of the plications is nowadays a little bit 122)#23&1'%&0)-#,&1$(+/ ?)($%&)($+,-#+-#(#"2!/. reasons why we decided that different, maybe because they ,%+041&/5 8&1-2/@-# .()&@A# B-# +$ maybe our son should go to the are developing. So to me, now, Mathematical education is of $1!&: Hungarian system. the exciting general question in course a difficult thing and every There is some truth in that, but Mathematics is easier for young applied mathematics is to under- country tries a different method. it is not that simple. When I was people because you don’t need stand complex large structures. There are some big swings but young, I had the great fortune of equipment. In many sciences That seems to be where the ap- not necessarily in the good direc- being able to meet Erdös fairly you have to fight for this equip- plication of mathematics is head- tion. regularly and sit in the room with ment and then of course senior- ing. other people and get these prob- ity and influence and And also possible applications 62&-#'+//+/.#+/#)($%&* lems. I got the mathematical connections and other things in history or something where )($+,(0#70")8+(4-#(--!1& problem and I never questioned matter much more. On the other you have a structure of interact- $%($#"2!#9&,2)&#(#.224 it. I thought that if Erdös asked hand, in mathematics it is impor- ing people. History is determined 1&-&(1,%&1: the problem, it must be an impor- tant to have an environment by how ideas or inventions or re- There is a very strong correla- tant problem and I started to which tells a young person what ligions or diseases are spread- tion. Of course, people have all work on it. Nowadays I have to to think about and what are the ing. This is a complex structure sorts of problems and also lose figure out which problems are important problems and what is which we are starting to under- interest or become interested in important. I think over sixty, one the direction in which the science stand but we don’t really have an something else.But if you look at has more experience, and there- of mathematics goes. I should established theory. Of course the Math Olympiad gold medal- fore maybe I can help in this re- say, luckily, the culture in mathe- there is brain research or internet ists, a very large number of them spect to figure out which matics is quite good in this re- research or ecology or global became leading mathemati- problems are important. Maybe spect. So, senior people are warming. In all of these, the trou- cians. the style of doing mathematics is usually not only willing but quite ble is there are very large struc- a bit different for older people eager to get younger people tures where you cannot just write ;1&#-2)&#,2!/$1+&-#($#(/ and younger people but at least working. If there are good senior up a few equations and solve (43(/$(.&#'%&/#+$#,2)&- for a while I would like to do people around, young people will them and that tell you what’s $2#)($%&)($+,(0#1&-&(1,% mathematics and I hope I can do get those problems. And there’s going to happen. So that’s what ,2)8(1&4#$2#2$%&1-: it in a useful way. more time because old people to me a big challenge in front of Mathematical research may be Mathematical talent is actually have a lot of responsibilities be- mathematics is. a good area where countries can

Bailing out : !"#$%&'()"*&+#&,-. An ode to the prime number A young mathematician was 09:30 -1 2 :30, Halls 3 & 4 - Ope ning Ce remony theorem : visiting the university of Chicago and was unfamiliar Aw ard of Fields Med als and the N eva nlin na, Gauss a nd C hern - Numbers in their prime as yet with the local ways of Prizes for no reason or rhyme communication. 12:30-1 4:00 - Lunch show up at a rhythm Walter Baily came up and in- with probability 1/logarithm. troduced himself briefly as - 14:00-16 :30, H all 4 - La udations If this is a law they knew, ``Walter Baily" to which the they also break quite a few visitor replied, ``no ! no! I am Chair: J. Palis Jun io r but that is not a crime! so-and-so." 14:00-14:25 Work of Elon Lindenstrauss After Baily smiled and left 14:30-14:55 Work of Ngô Bao Châu Newsletter Team him, the visitor caught hold of 15:00-15:25 Work of Stanislav Smirnov someone nearby and, point- 15:30-15-55 Work of Cédric Villani R. Ramachandran ing towards Baily, asked 16:00-16:25 Work of Daniel Spielman B. Sury ``could you tell me who that Geethanjali Monto all 4 - Abel Lecture is?" 16:45-17:45, H Richa Malhotra Midhun Raj U.R On being told that the person S. R. S. Varadhan, Courant Institute of Mathematical Sciences, Mohammed Anvar T was Walter Baily, the visitor New York University, USA Rahul V. Pisharody quipped, ``but he thought I Large deviations Sidharth Varma was Walter Baily!" Chair: K. R. Parthasarathy Nikhil M.G