A Trio of Institutes Allyn Jackson

“[I]nstitutes for advanced study Aarhus University modeled in some measure or Svend Bundgaard is not a household name among another along the lines of the mathematicians. Looking him up in MathSciNet Princeton Institute are [multiply- reveals that he published just seven papers in ing] and will multiply throughout his lifetime. He does not appear at all in the the western world.” Mathematics Genealogy Project because he had — J. Robert Oppenheimer, in a no Ph.D. students—and in fact did not have a December 17, 1959, letter to the Ph.D. himself. And yet Svend Bundgaard had a French Education Minister, sug- significant impact on mathematics by establishing gesting the French government Aarhus University in Denmark as an internation- support the Institut des Hautes al focal point for mathematics research, with a Études Scientifiques thriving visitor program and excellent facilities. The traditions he fostered there starting in the In mathematics, Oppenheimer’s prediction has 1950s have continued ever since and find their come true: Over the past couple of decades, math- most recent expression in the establishment of ematics institutes have proliferated worldwide. two centers within the mathematics department, While all share the goal of fostering mathematics the Center for the Topology and Quantization of research, each has its own unique history and tra- Moduli Spaces (CTQM) and the Thiele Center for ditions. Europe boasts several major institutes that Applied Mathematics in Natural Science. loom large in international mathematical affairs, Bundgaard was born in 1912 and received a from the elegant Institut des Hautes Études Sci- master’s degree in mathematics from the Univer- entifiques, whose activities are mainly organized sity of Copenhagen. On the faculty at the time by its small but outstanding permanent faculty, to were the physicist Niels Bohr and his brother, the beloved Mathematisches Forschungsinstitut in mathematician Harald Bohr, and the two made Oberwolfach, Germany, a bustling conference cen- Copenhagen a lively center for mathematics and ter with a different event every week. But Europe physics. It was there that Bundgaard made con- also has several smaller institutes known for their tacts with leading mathematicians from around high-quality mathematical programs and their dis- the world. In 1954 he became the first mathe- tinctive characters. Three of them are profiled here: matician to be appointed to Aarhus University’s the mathematics department at Aarhus University division of science, which had been established a in Denmark, the Centre de Recerca Matemàtica in few years earlier (the university itself was founded Barcelona, and the Centro di Ricerca Matematica in 1928). There was no mathematics building; a Ennio De Giorgi in Pisa. small office was cleared out for him in the anatomy building. But Bundgaard had been hired to launch the mathematics department, and for this he had Allyn Jackson is senior writer and deputy editor of the big plans. From the beginning he envisioned an Notices. Her email address is [email protected]. international dimension for the department, and

1426 Notices of the AMS Volume 56, Number 11 when he got funds to hire faculty, he used some of the money to bring in long-term visitors from abroad. Bundgaard’s genius for administration can be seen most clearly in the current mathematics de- partment building, which was completed in 1967. Aarhus mathematicians say that Bundgaard sat in on all the weekly meetings of the architects and builders to make sure that the design features he wanted were carried out. When higher-ups nixed his plan to install sinks in all the offices so that people could wash chalk dust from their hands, (Photo courtesy of Masaaki Suzuki, Akita University.) Bundgaard had the builders put the sinks in any- The entrance to the mathematics building at way; they are discreetly hidden behind cabinet the University of Aarhus. doors, possibly to avoid being seen by govern- ment inspectors. In another instance of bucking authority—and one that could not be so easily hidden—he directed the builders to put guest still produced in the Aarhus department. Because rooms and apartments on the top floor of the of these long-standing exchange arrangements, mathematics building, even though the authoriza- the library has some rare journals that one typ- tion for this construction had been turned down. ically does not find in a standard mathematics It was a prescient move: having these lodgings library. Aarhus mathematics faculty member Jo- available made it easy for the department to invite han Dupont recalled that in 1969, when he was a many short- and long-term visitors from abroad. graduate student at Aarhus, he attended a confer- A set of apartments was also added to the com- ence in Bucharest and was put up in a fancy hotel puter science building when it was constructed. room after telling the conference organizers where The Aarhus mathematics department today has he was from. Thinking of their journal exchange ar- sixteen guest rooms and six apartments. rangement with Mathematica Scandinavica, “they The mathematics building is a lively place, mistook me for an Aarhus bigwig,” Dupont said bustling with faculty, students, and visitors. “The with a laugh. Three years later, Dupont became a infrastructure fills all of our needs,” states depart- coordinating editor of Mathematica Scandinavica ment chair Johann P. Hansen. Apart from some interior renovations to spruce things up—and the and served in that capacity until 1988. sacrifice of a couple of seminar rooms to office For those who have become accustomed to li- space as the department grew—the building re- braries outfitted like airport security checkpoints, mains as it was in Bundgaard’s day. Each floor has the Aarhus library evokes amazement. Anyone can several small spaces equipped with blackboards, walk in, browse around, find books and journals tables, and chairs, where people can gather and on the shelves, and photocopy materials. It is not chat. The “mathematics canteen” on the first floor a quiet place: the first floor is the math lab, filled attracts students and faculty from within and out- with students sitting at tables discussing math side the department. During a two-week CTQM problems. The one rule is that books must not be workshop in 2008, fifty mathematicians from all removed from the math building. Inevitably, some over the world, including a large contingent from material is lost. But according to Hansen, so far it Japan, attended talks in one of the building’s larg- has proved less expensive to replace the missing er lecture halls, milled around the corridor during material than to hire a gatekeeper. coffee breaks, and mixed with students in the Thanks in large part to Bundgaard, the Aarhus canteen for lunch. The proof of the genius that mathematics department has all the facilities need- went into the building’s design can be seen in the ed to function as a small mathematics research use to which the building is put: many different institute. What it does not have is the money to kinds of activity comfortably coexist. support such an enterprise—in fact, the university Bundgaard knew that a high-quality mathemat- provides little funding to support research. For ics library was needed to support research in the this reason, Aarhus mathematicians have long pur- department, and for this he secured funds from sued outside funding from the Danish government the Carlsberg Foundation, which was created by the Carlsberg beer brewery in part to support and other sources in order to host institute- scientific research. Today the library has about like activities within the mathematics department. 100,000 books as well as subscriptions to more One of the best known of these enterprises was than 400 journals. Some of the journals come MaPhySto, which stands for Mathematical Physics in exchange for Mathematica Scandinavica, which and Stochastics. In its initial incarnation, MaPhySto is another initiative of Bundgaard’s and which is ran from 1998 until 2003, with a five-year grant

December 2009 Notices of the AMS 1427 1428 (Photo courtesy of Masaaki Suzuki, Akita University.) anig nteAarhus the in paintings ahmtc building. mathematics hsprri fSvend of portrait This B ngadi n of one is undgaard eea interesting several rn rmteDns aua cec Research Science Natural Danish with the 2006 from in grant of began a Quantization which (CTQM), and Spaces Topology Moduli the for Center the orga- and each and conferences year. seminar and students, workshops four weekly Ph.D. about nizes for a courses runs Re- intensive center Strategic for The Council search. Danish the and Research Council Science Natural center’s Danish the the Ph.D. from through funding and supported universi- researchers are postdoctoral who the students as of well departments as ty, various in permanent faculty including has members, center twenty-five The about bioinformatics. and stochastics computation- al processes and stochastic modeling, spatio-temporal probability, ge- and theo- applied stochastic Lévy and analysis, are science. ry image emphasis statistical natural inter- of and of ometry its areas disciplines and main other stochastics The focuses with in center Math- play research The Applied basic Science. for on Natural Centre in Thiele new ematics a for the proposal a initiative, with ready were department Ph.D. many supported students. and post- researchers for program doctoral active and an semi- conferences had also many ongoing It workshops. organized an and held series, nar visitors, short-term long- of and hundreds MaPhySto drawn had time it the operations, By ceased probability. ma- free stochastic and systems, trices, particle anal- interacting stochastic ysis, as stochastics—such of areas theory— and field mechanics, quantum and quantum mechanics, math- statistical as of physics—such areas ematical between collaborations ciplinary h aetadto oteAru eatetis department Aarhus the to addition latest The Aarhus the of members ended, MaPhySto When interdis- spurred MaPhySto lifetime, its Over cossvrluieste in Denmark. universities several stretching across network a being Aarhus at to located be- center a from of ing changed structure suc- the MaPhySto and his cessor, Aalborg became of Jensen University the Arne up MaPhy- Sto. of give director to of position had in he 2003, retired When Barndorff-Nielsen stochastics. department’s in strength the figure building key in mathematics a and Aarhus department the member of E. a Ole Barndorff-Nielsen, was director and scientific founder The Research Foundation. National from Danish rate) the the exchange at kroner million current million US$6 50 (around about of N tcso h AMS the of otices oa ponmns Ti sagetopportunity great a postdoc- is and “This predoctoral appointments. joint toral for component include will a institutions coop- two latter The the with Kontsevich. eration Maxim Institut through of the Paris, involvement in to the Scientifiques and of Études Hitchin, University Hautes Nigel des the by at led group Oxford, geometry new the support be- to to ties and links the Berkeley UC strengthen and The further CTQM years. tween to five se- help coming CTQM, will the grant to for funding boost This its significant kroner. curing million a 50 provides of Research grant total National a Danish for the Foundation from grant lence” visitors and long-term year. distinguished postdocs, each of eight handful a and a for visitors six has senior funding between 100 hosts over overall year, has Bohr center boosted Niels The the greatly year, CTQM. students, every has his period of grant bringing a some to with for along addition Aarhus In to Reshetikhin workshops. confer- and visitors, ences, other some researchers, positions, a temporary postdoctoral additional for two support for fund- ing with of along years professor, visiting five distinguished Na- provide Danish Niels grants center large-scale the Bohr The from the Foundation. grant Research whom Bohr tional for University Niels the Berkeley, a secured of at Reshetikhin California Nikolai of of of that University to the at position Aarhus; a at took longer Copenhagen. he no 2008 is Madsen in curves. moduli of the of space cohomology stable the David of on conjecture Mumford a of Weiss, Michael 2005 with his proof, topology. after years longtime recent in in rose strength a profile for Madsen’s department’s Madsen, responsible the largely Ib was building as who well member faculty as Dupont, Andersen and vari- including department, of the interests in research people ous the with well meshed it of areas different many with mathematics.” focus interacts The have things. other spaces, we various moduli study of to topology need the you remarked. study he to on,” order so “In and theory, gauge of many includes aspects it topology, quantum spaces of all moduli includes of connects “Quantization area subjects. the other time, a to same us gives the to it At and profile.” study, move clear we very things of emphasizes interesting kind it the because an much focused, very was Andersen it “it make Ellegaard that Jørgen nar- explained director rather sounds CTQM this row, If groups. their class and mapping surfaces two-dimensional to spaces moduli investigation associated of quantization the and on topology the focuses of center The Council. n20 nesnrcie cne fexcel- of “center a received Andersen 2009 In connects also CTQM of focus research The that is chosen was area this reason the of Part Volume 56 Number , 11 for us here at CTQM in Aarhus to be able to co- operate with these world-renowned mathematical research institutions in this very manifest way,” said Andersen. Enterprises like CTQM and the Thiele Center have strengthened the international dimension of mathematics research at Aarhus. But such large- scale efforts exact a cost: The funding is always temporary, and there is a constant struggle to make sure new grants are lined up when the old ones run out. They also put additional pressure on the department’s resources and infrastructure. Another consideration is how well these cen- ters serve home-grown Danish doctoral students. Dupont, who is a member of CTQM and recognizes the value it brings to the department, nevertheless noted that only a few of the department’s doctoral (Photo courtesy of D. Kotschick, Ludwig-Maximilians-Universität München.) students have the background to really benefit from all of the activities hosted by the center. The entrance to the main lecture room of the The department will face a wave of retirements CRM Barcelona. in the next few years, and having the Thiele Center all be the work of a good architectural firm. But and CTQM will certainly make Aarhus more attrac- when one notices the way the classic motif of the tive to job seekers from other countries who might CRM logo is carried throughout the space on the not otherwise consider making the leap to a small etched glass that adorns the doorways, and when Scandinavian country with a difficult language. one notices the eclectic, often arresting works of And these foreigners will likely be needed. During art, one discerns a personality behind the CRM. a recent stint as director of the graduate program, That personality is Manuel Castellet, the Dupont did a survey of Aarhus Ph.D.s in mathe- founder of the CRM and a professor of mathemat- matics over a period of ten years and found that ics at the Autònoma. He started the center in 1984, only one-quarter of them ended up with academic a time when the mathematical culture in Spain jobs in Denmark. “We might get into difficulties if was just starting to recover from the isolation we want to have enough Danish mathematicians,” imposed by the dictatorship of Francisco Franco, he noted. Although he recognizes the value of which lasted from 1936 until Franco’s death in cultivating a strong international research envi- 1975. During the Franco era, Spanish universities ronment in the department through ventures like emphasized personal and political connections CTQM and the Thiele Center, Dupont cannot help rather than excellence and merit, and in this but wish that funding were also available to ad- atmosphere mathematical culture languished. dress more local problems, such as improving the This was no less true in Catalonia, a center of academic career path for young Danish mathe- resistance against Franco, than in the rest of maticians. The goal, as Dupont put it, should be to Spain. “If you look at Mathematical Reviews from create something with “a long life in mathematics”. the end of the 1960s and beginning of the 1970s, No doubt Svend Bundgaard would agree. there are no papers by Spanish mathematicians,” remarked Castellet. “During the 1960s and 1970s Centre de Recerca Matemàtica Barcelona at the University of Barcelona, only one Ph.D. in The student unrest that gripped the world dur- mathematics was given. And this was not much ing the 1960s led to a university building boom different from the rest of Spain.” across Europe. In Catalonia, the historic Universi- At that time, a small number of Spaniards went tat de Barcelona, founded in 1450, was joined by abroad to get Ph.D.s in mathematics, with the two modern campuses, the Universitat Politècni- idea of returning to their native land and build- ca de Catalunya and the Universitat Autònoma de ing mathematics research there. Castellet was one Barcelona, both of which were established in 1968. of them. He went to the ETH (Eidgenossische Located in the suburb of Bellaterra, the sprawling Technische Hochschule) in Zürich, where he re- campus of the Autònoma abounds with the boxy ceived a Ph.D. in 1973 under the direction of Beno concrete buildings characteristic of its era. Though Eckmann. About a decade before, Eckmann had the mathematics building is just as unprepossess- founded the Forschungsinstitut für Mathematik ing as the rest, in one wing it houses an oasis of (FIM), a research institute in the ETH mathematics elegance called the Centre de Recerca Matemàtica department that to this day remains a well-known (CRM). The judicious use of space, the refined international center. Castellet stayed on for two lighting, and the fluid, undulating corridors could years as a postdoc at the FIM, where, he said, the

December 2009 Notices of the AMS 1429 1430

(Photo courtesy of D. Kotschick, Ludwig- topeews“atsi” twstemeeting the was it p “fantastic”: was atmosphere acln,wihi bu hryfiemntsaway of minutes center thirty-five the Vallès, about in is del which hotels Barcelona, Cugat in rents or San CRM housing, nearby university the in in apartments purpose of they that set Instead for a visitors. in for lodged housing are CRM on-site the no Aarhus, has in Unlike confer- workshops. in and programs, ences, research bring organize Autònoma—could and visitors the lo- and three the Politècnica, Barcelona, the de at Universitat universities—the mathematicians cal which in forum years). recent in changing been the has Europe Catalonia of this in that outside (though Spain greater argued in than been Spain be has of outside could CRM the It of programs. influence its only in participat- the Spaniards ed non-Catalan years few many very Spain, in for mathematics for institute been visitor’s international has it community. international Although local the and, the to Barcelona service to in secondly, service mathematicians CRM all, of The of community IEC. first late the emphasized, the from has Catalan since than the has from rather its funding it government retains core though its even CRM received IEC 1980s The the culture. Cata- to to ties and related language areas in lan the strong- research organization within promotes an a founded that (IEC), had Catalans was has d’Estudis It Institut Catalan too character. more CRM Catalan ly as The themselves Spanish. than of many and think identity, cultural Catalans strong a and Spanish, rich as a not are on Swiss.” “We the designed—though as Castellet, was Said scale. CRM smaller the model for which the needed became on FIM Barcelona The thrive. what to at exactly mathematics stimulating were so FIM found newly the had the he inter- at contacts the that national position return realized a his He Autònoma. took Upon established world. Castellet the Spain, over to all from others Maximilians-Universität München.) itfrmteaiin nZrc n attracted and Zürich in mathematicians for oint h oeo h R a ent rvd a provide to been has CRM the of role The from distinct language, own its has Catalonia ordri h R Barcelona. CRM the in corridor A N tcso h AMS the of otices h em ftecnrc,teCMbgnissuing began CRM the contract, the of be- terms Under discussions center. the in the Previously, and mainly mathematicians run. made local tween were been CRM hold had the to programs at CRM research which the about decisions way changes brought the also in contract The stable more funding. out; and core larger carried received be CRM the to return, in objectives strategic to specified and that had duties government center the with the contract the so, a sign and do CRM IEC To the the government. 2002 Catalan between In “consortium” that years. a opportunities recent became new in on appeared al- capitalize have has to that it institute lowed well-established well-run, a mathematics supporting in Europe. across active institutes Castellet been Society), also committee Mathematical has European a the (European Mathematics, of ERCOM on Centres establishing the Research in of one players As main Catalonia. in to helped mathematics has years develop the over CRM careful the Castellet’s of cultivation that clear seems it on views, dis- parate focus these Despite to excellence. and funds strength of scarce areas its had husband CRM carefully the that to argue on Others at- breadth. focus to insufficient tention its an a constituted particularly on topology, areas, focus algebraic CRM’s of the range that limited say mathemati- Barcelona and Some in 2002 volumes). cians in ten started some was comprises which Barcelona”, CRM Mathematics, pub- in Courses also “Advanced series, (Birkhäuser a lishes Birkhäuser and series Springer book of spread in proceedings also of was publication conferences through the area. of that influence in The working mathematicians local a the in- stimulus for much as topology providing algebraic map also in while the ternationally, research on for Barcelona point the put focal in con- helped experts These top and the 2002. area CRM of to the some 1986 attracted at from ferences held Algebraic years meetings four on of every Conference series a Barcelona be can Topology, the area in algebraic latter the of seen on area emphasis own mathematicians, The Castellet’s topology. local in strong particular are in there which in occupies. existing now the center to the building, meters 1,200 a mathematics square build 900 the to another to adding plans adjacent now wing are new there in and running crowded years, center increasingly recent become the their has keep know It and who smoothly. and out staff and comfortable, dedicated inside a jobs and has modern center the are The offices Catalonia. books in CRM to network access interlibrary good an to has through subscribes and which journals mathemat- 250 Autònoma, its the about the have on of relies not library instead does ics but CRM library The own train. commuter by ti xcl h utvto fteCMinto CRM the of cultivation the exactly is It areas emphasized has CRM the years the Over Volume 56 Number , 11 formal calls for proposals open to mathemati- what is being done” in the university mathematics cians all over the world and established a clear departments in Barcelona. decision-making process by the CRM’s Scientific The strategy the direction team is pursuing Advisory Board. As a result, a broader range of is to have “semi-permanent” research positions: areas has been represented at the CRM in recent one or two long-term researchers would be hired years: Research programs have included geomet- each year in areas not currently represented in ric flows, enumerative combinatorics and random the local universities. After taking a few years to structures, Arakelov geometry and Shimura va- build up research groups in those areas, these rieties, and control theory. In addition, through CRM researchers would be expected to move on a European Union project called NEST (New and to permanent positions in academia, or, in ex- Emerging Science and Technologies), the CRM has ceptional cases, at the CRM itself. The center has hosted programs to foster international collabo- now established a few such positions and has a ration and training in three emerging subjects: search under way to add a researcher in industrial risk assessment, mathematical neuroscience, and mathematics. The strategy the CRM has pursued digital content security. for these positions is similar to that of ICREA, Castellet retired as director in 2007, and, after a widely praised program of research positions an international search, his Autònoma colleague that was put in place by the mathematical econo- Joaquim Bruna was named as successor. When mist Andreu Mas-Colell when he was Minister for Bruna began as director, everything was in place Universities and Research of the Government of to run a successful international mathematics in- Catalonia from 2000 to 2003. ICREA was so suc- stitute. “That’s terrific,” said Bruna. “That’s some- cessful that it has been replicated in other regions thing that has a lot of merit.” Today Castellet holds in Spain. the title of honorary director, by decision of the Another area of expansion in the CRM in the Board of Governors in recognition of his achieve- past couple of years has occurred in its postdoc- ment in founding and building the CRM. Bruna has toral program. Since 2000 the CRM has been a begun to put his own stamp on how the CRM is run participant in the European Postdoctoral Institute and has set up a team of three codirectors from the (EPDI), which provides two-year grants for young other Barcelona universities: Marta Sanz-Solé and mathematicians to visit at least two of nine mathe- Carles Casacuberta of the Universitat de Barcelona matics institutes in Europe for six- to twelve-month and Joan Solà-Morales of the Politècnica. A group stays. The CRM also now funds its own two-year of dynamic and experienced academics like this postdoctoral positions. These have been in de- one is not going to agree on everything. But all are mand, last year attracting a total of sixty-three committed to preserving the traditions that have applicants for just four slots. Altogether, with made the CRM successful in the past while con- funding from various sources, the CRM last year tinuing to expand its international presence and hosted a total of twelve postdocs; the stays were the mathematical areas represented in the center’s of varying length, partly due to variations in the activities. The CRM has also renewed its Scientific funding of the positions and partly due to some of Advisory Board to make it more international and the postdocs having found permanent positions more involved in decisions about the directions before their time at the CRM had ended. the center takes. Overall, support for mathematics and science The main purpose of the CRM is still to pro- in Spain seems to have a bright future, part- vide a home for activities, such as conferences ly because of insistence by the European Union and year-long research programs, that local math- that its member states invest a certain percent- ematics departments cannot easily carry out. At age of their gross national product in research. the same time, the center is trying to promote new In 2006 the Spanish government funded Ingenio directions that the universities do not have a way Mathematica, or i-MATH, a five-year, C7.5 million to promote. As Bruna put it, the CRM today is “at (approximately US$10 million) project designed to somewhat of an inflection point.” When it became a enhance and unify mathematics research across consortium center under the Catalan government, all of Spain. The CRM is one of five nodes partici- the CRM joined the CERCA network of thirty-eight pating in i-MATH, and Bruna sits on the project’s research centers in Catalonia—and the CRM was direction board. The establishment of i-MATH has the only center in the network to have no per- enhanced the influence of the CRM within Spain. manent research staff. The new contract that the In the last couple of years plans have been under CRM negotiated for 2008–2012 stipulates that the development for the establishment of other math- center must appoint permanent staff. This means ematics institutes in Spanish universities as well a big change but also a big opportunity, Bruna not- as a national network to connect their activities, ed. “We have thought a lot about this, about how and some of these initiatives have gotten off the to match this with the typology [of the CRM],” he ground. said. “We want to go in this direction, but always In April 2009 the CRM kicked off a celebration with the idea of supporting and complementing of its twenty-fifth anniversary, with the president

December 2009 Notices of the AMS 1431 1432

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Centro at Normale by used Scuola not be the can do but they Centro the since to exclusively especially belong to kitchen- demand, needless high nine in are, say, which has rooms, eleven palazzo sleeping equipped tall with The and offices. easily modern beams combine ceiling windows interior shuttered wooden elegant reno- rustically exposed on a deciding where is in result freedom Centro The of vations. the deal good so a exceptional, had architecturally not is substantial De records. with Centro track institutes the many were mathematics model, there when a existing time a as at started take was to Giorgi Zurich the in beyond in founded exemplars FIM few was with which 1984 CRM, in Barcelona the unlike in And Centro universities Pisa. three the from research, funding essen- for steady university receives funds in no the Also provides where directly tially building. Aarhus, Pisa, main to in Scuola’s contrast Cavalieri the dei from Piazza across the which the on Puteano, provided sits Palazzo Normale Scuola 17th-century the handsome Aarhus: Bundgaard as in building, new did a build to need no an there was example, had For ground. has the off ways getting time some easy Italian in the Centro from the funding government, of lack in the launched Despite been 2001. having institutes, mathematics world. the around from mathematicians leading the from with has programs it high-powered that organized and beginning especially Italy only in kind the is its is of Centro institute government the that the considering surprising from some said. silence he me—just reaction,” negative The for a already even answer reaction, would of positive sort a that we been interesting’, and have doing it’s are think you don’t what considered saying, have research] and ‘We from universities Giaquinta’s letter of a ministry Rather, had [the I “If Centro. ignored. simply the are against inquiries to decided has funds government the giving that government. is not Italian is him the It from puzzles response really of lack what the did But as down, Florence. him turned nearby of Centro, government the to city home the Pisa, Even Giorgi. De Centro the support to Tuscany several in get nearby are to that communities success without tried has Giaquinta postdocs.) the unable fund be to would continue town due to the that, difficulties, Giaquinta financial informed to Lizzanello end: 2008 tales In happy no, (Unfortunately, town them it.” tell does the I town that And the say way.’ law that some money they spend be cannot story], must ‘There [this say, it them, they people tell I tell possible.’ Giaquinta. not ‘That’s said I amazing,” time really “Every is “It postdocs. h aaz uen salvl uligbut building lovely a is Puteano Palazzo The newest Europe’s of one is Giorgi De Centro The case. special a been have to seems Lizzanello Volume 56 is osbe And possible. Number , 11 said are “too few, not very good, and expensive.”) scientific reports of the director, are available on The larger of the building’s two seminar rooms the Centro’s website.) holds only about thirty people, but bigger lecture From the start the Centro has attracted top halls are available at the Scuola Normale. Surpris- mathematicians. The first intensive research pe- ingly, there is no wireless network in the building, riod, organized in 2002, lasted two and a half but this might not be a disadvantage: the wired months and had about eighty participants. It fo- Internet connections in the offices are faster and cused on dynamical systems and was organized by more user-friendly than the wireless networks at a scientific committee, including two Fields Medal- Aarhus and the CRM. Keeping the place running ists (John Milnor and Jean-Christoph Yoccoz; the smoothly is the friendly and efficient two-person other members were Stefano Marmi, John Mather, staff, Cecilia Cappelli (who replaced Ilaria Gabbani and Jacob Palis). Giaquinta pointed to the 2005 in fall 2008) and Antonella Gregorace. research program in Diophantine geometry as one The Centro’s largest source of funding is the of the Centro’s best so far; with seventy-five par- Scuola Normale, which provides C200,000 per ticipants over a four-month period, the program year (financial difficulties reduced this amount to was organized by Yuri Bilu, Enrico Bombieri, David C150,000 in 2009); the University of Pisa, just Masser, Lucien Szpiro, and Umberto Zannier. The across town, contributes C100,000, and the Scuo- intensive research program in 2007, on dynamical la Superiore di Studi Avanzati Sant’Anna, a newly systems and number theory, was especially large, established university for applied research, chips with a total of over 200 participants. Organized in C50,000. These funds come with very few re- by Grigori Margulis, Stefano Marmi, Peter Sarnak, strictions, so Giaquinta has plenty of flexibility Jean-Christoph Yoccoz, and Don Zagier, it includ- in how he can use the money. The Centro also ed a workshop for 100 graduate students that gets smaller amounts from other sources. One is was funded by the Clay Mathematics Institute. The the Istituto Nazionale di Alta Matematica, which total number of mathematicians coming to the is the main funder of mathematics meetings in Centro per year has increased over time, hitting Italy and which the Centro can turn to for support 800 in 2007. for specific programs. A few Italian universities Local expenses are provided for all participants, whose mathematics departments want to support including meals at the Scuola Normale cafeteria— the Centro have contributed small amounts, and and, this being Italy, the food in the cafeteria is a foundation connected to a bank in the Tuscan quite good. Many participants are able to fund town of Lucca gives the Centro around C15,000 their travel through grants, and for those who per year. Organizers of the programs often use cannot, the Centro can sometimes help with trav- money from their research grants to pay for travel el expenses. For visitors who stay for at least a and housing for students and other participants. month, Giaquinta said, the Centro provides “a kind By cobbling together these sources of support, of salary”—but not a full salary, as the Centro does the Centro runs fairly well on its total budget of not have enough money. In fact, Giaquinta said about half a million euros per year, Giaquinta said. that one of his dreams for the future of the Centro “But we could do much better with one million.” is to have more long-term visitors who stay six to His unsuccessful efforts to get the attention of twelve months, so that there is deeper and more the Italian government centered on bringing the sustained activity. But this would require having, budget up to that level. say, three or four long-term visitors who could Giaquinta said that the Centro is based loosely interact—and that is much more than the Centro on the model of the Newton Institute in Cambridge, can afford right now. England, though the Centro is much smaller and As director, Giaquinta has a great deal of lat- more informal. “There are no very strict regula- itude in making decisions about the activities of tions concerning how the institute can be run,” the Centro. There is no committee to evaluate pro- he noted. Indeed, since the Centro’s inaugural posals for programs; in fact, there is no formal call activities began in early 2002, it has had a fluctu- for proposals. So how does one apply to organize a ating mix of “intensive research periods”, which research program at the Centro De Giorgi? Pick up last a few months, and shorter workshops, which the phone and call Giaquinta. But the Centro is not run for up to a week. In 2003 there were four a one-man show. Giaquinta consults widely with intensive research periods and one workshop; by many colleagues, especially those in the Scuola 2007 the balance had nearly reversed, with one Normale, about what activities would be best to intensive research period and fifteen workshops. host. And he does not simply sit back and wait The Centro also sponsors “research nuclei”, which for calls to come in; he actively pursues ideas for are small groups of Italian mathematicians who program topics and persuades people to serve as are working together on a long-term basis and who organizers. This highly flexible style seems to suit use the Centro as a place to meet and collaborate. the small size of the Centro and allows it to put a (Descriptions of past, present, and future activities premium on quality. Giaquinta and his colleagues of the Centro, including the annual financial and at the Scuola make most of the major decisions

December 2009 Notices of the AMS 1433 about directions the Centro takes, leading to some symbolizes the long heritage of mathematics in grumbling on the part of mathematicians at the Italy. It is therefore surprising to find that the Ital- University of Pisa, who see their institution con- ian system for supporting research and for funding tributing a tidy sum to the Centro and sometimes enterprises like the Centro De Giorgi is weak. “You feeling a bit distant from its activities. have isolated good situations, but the entire sys- One program for which the Centro does have tem doesn’t work,” Giaquinta remarked. “That an organized call for applications is the program is typical of everything—mathematics, physics, for “junior visitors” (these are essentially post- medicine. The system is very bad.” What saves it, doctoral positions, but the word “junior” is used he said, is that “there are some very good people to circumvent Italian government regulations re- around.” lating to positions referred to as “postdoctoral”). These positions are in high demand: In 2007 there were about 100 applications for just three or four positions. Only five of the applicants lived in Italy (applications also came from Italians living outside the country). The reason for the lack of applica- tions in Italy could stem from the hiring traditions there, which remain extremely local. The usual method of filling positions is to pave the way for a local candidate, rather than hiring someone from outside. Such inbred hiring traditions mean that a postdoc at the Centro is not especially attractive to a young Italian mathematician whose long-term plan is to stay in Italy. The restricted hiring opportunities in Italy have caused some “brain-drain”. In particular, new Ph.D.s from the Scuola Normale—which traditionally has attracted some of the most talented students from across Italy—are at a disadvantage, because the Scuola has very few positions in mathematics, and the Scuola Ph.D.s are often considered as outsiders by other departments in the country. As a result, some of the best young Italian mathematicians have ended up outside their home country. Simon Salamon of the Politecnico di Torino was on the organizing committee for two programs at the Centro De Giorgi, including a large one in 2004 that ran for three months. He is an enthusiastic supporter of the Centro. There are several venues in Italy that have become traditional sites for mathematics conferences and short courses, but the Centro offers the possibility for longer-term activities. “There is nothing else like it in Italy,” he said. Having the Centro in Pisa not only offers ease of access from most parts of Italy and from many cities abroad, but it also takes advantage of the fact that Pisa is, and long has been, a vibrant center for mathematics. “Pisa is one of the cities that has traditionally been important in mathe- matics,” noted Salamon. “You only need to go to the camposanto [cemetery] and see the graves of mathematical giants.” One indication of Pisan traditions in mathemat- ics is the statue of Ulisse Dini (1845–1918), which stands just across the plaza from the Centro. Dini was on the faculty of the University of Pisa, and late in life he became the director of the Scuola Normale. That he was also a member of the Italian Parliament might be the reason for his memori- alization in a statue, yet the statue neverthless

1434 Notices of the AMS Volume 56, Number 11