Scientific and Administrative Report 2001_2005

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2 Scientific and Administrative Report 2001_2005 SCUOLA NORMALE SUPERIORE Scuola Superiore Sant Anna

3 Preface

4 The Centro di Ricerca Matematica Ennio De Giorgi, Matematica nelle Scienze Naturali e Sociali, was established at the end of 2001 as a center of the Scuola Normale Superiore, with the character of an inter-university center, by the three university institutions of Pisa. With an Agreement signed by the Rector of the University of Pisa, Luciano Modica, by the Director of the Scuola Superiore Sant Anna, Riccardo Varaldo, and by the Director of the Scuola Normale Superiore, Salvatore Settis, the Center was given a grant for five years through December 2005, so that it could operate, planning its activities well in advance. This is the scientific and administrative final report concerning the first five years of activity of the De Giorgi Center. The Rector and the Directors of the founding institutions have in fact agreed to extend the agreement with the Center for the next five years, until December, The report is divided into three parts. In the first part, after a few remarks about the reasons for establishing a research center in mathematics and establishing it in Pisa, I describe its structure and aims, and I report on the scientific activities held the Center year by year and on the related financial issues, also presenting the annual balances. As a conclusion of this first part I formulate a few comments about the past and the future of the Center on the basis of the first five-year experience. In the second part I collect the scientific reports regarding all events, essentially in the form they were prepared by the scientists in charge of each event. The third part contains a list of all visitors of the Center. Because of the international character of the Center, more than seventy per cent of the visitors were non-italian, in order to facilitate the reading of this report for the members of the Scientific Committee, which acts both as an advisory and as an evaluating committee, this report is written in English except for a few instances where I preferred to stay with the original languages. The activity of the past five years would not have been possible without the scientific, financial, and administrative help of several people and institutions. Usually, this is the place to thank all of them; I have chosen to have acknowledgements as part of the report, at the end of part one. The Director of the Center Mariano Giaquinta 5 Scientific and Administrative Report 2001_2005

5 1. The De Giorgi Center: Scientific Activities and Finance

6 1.1 Why support mathematics Why should anybody but mathematicians care about the standing of mathematics in the world? To lay-men, policymakers and legislators, the answer is far from obvious. In March 1997 the National Science Foundation in response to the Government Performance and Result Act of the United States and on the recommendation of the Committee on Science and Public Policy of the Academy of Science, the National Academy of Engineering and the Institute of Medicine, assembled a Panel to conduct an international assessment of the mathematical sciences. In March 1998 the Panel concluded its work with the Report of the Senior Assessment Panel for the International assessment of the U.S. Mathematical Sciences. We quote here a few passages from it. From the Executive Summary: The modern world increasingly depends on the mathematical sciences in areas ranging from national security and medical technology to computer software, telecommunications, and investment policy. More and more American workers, from boardroom to assembly line, cannot do their job without mathematical skills. Without strong resources in mathematical science, America will not retain its pre-eminence in industry and commerce [...]. Since the time of Pytagoras, mathematics has been one of the intellectual pinnacles of civilization. Although many mathematicians develop their subjects as purely logical structures, with no reference to the outside world, every area of mathematics, however pure it appears, has important applications: good pure mathematicians will always deserve support. For the benefit of the Nation and of U.S. mathematics, however, there must be more effective interaction between mathematicians and the users of mathematics [...]. The Panel recommend that the National Science Foundation encourages programs that Broaden graduate and undergraduate education in the mathematical sciences. Provide support for full time graduate students in mathematical sciences comparable with the other sciences. Provide increased opportunity for postdoctoral study for those who wish to become academic researchers, as a means to broaden and strengthen their training as professional mathematicians. Encourage and foster interactions between university-based mathematical scientists and users of mathematics in industry, government, and other disciplines in universities. Maintain and enhance the historical strength of mathematical sciences in its academic setting as an intellectual endeavour and as a foundation for applications. Some motivations: The fundamental changes taking place in many areas of science and technology - especially biology, communications, and computation - are accompanied by important new problems that cannot be solved without new mathematics. The modern desire to improve decision- making and to understand very complex problems will require original mathematical techniques. These deep challenges, which are vitally important to the nation, offer novel opportunities for research in mathematics. In an ideal world, mathematics has a clean flow from its core out to applications and from applications back to the core. This flow facilitates the adaptation of mathematical concepts from one field, such as physics, to economics, and vice versa. When mathematical sciences retreat from such multidisciplinary involvements, mathematics suffers from lack of enrichment by the ideas and chal- 7 Scientific and Administrative Report 2001_2005

7 lenges of other disciplines. The other disciplines also suffer, for two reasons: The disciplines lose the expertise and easy access to the vast knowledge base developed by the mathematical sciences; and The disciplines develop overly specialized mathematical language and tools that inhibit multidisciplinary communication [...]. The mathematical sciences are disciplines in themselves, with their own internal vitality and need for nourishment. But they also serve as the fundamental tools and language for science, engineering, industry, management, and finance. They are inextricably linked to these user fields and they frequently draw inspiration from them. The mathematical sciences represent a mode of thought based on abstraction that sustains precision and permits careful analysis and explicit calculation. Thus mathematics has a dual nature: it is both an independent discipline valued for precision and intrinsic beauty, and it is a rich source of tools for the world of applications. Mathematics might be described as having abstractness internally and effectiveness externally [...]. Although most of the mathematical research community is university-based, the impact of mathematics on society is pervasive. Mathematics underpins most current scientific problems in experimental sciences (biology, chemistry, geophysics, medical science), on government (defense, security), and in business (industry, technology, manufacturing, service, finance). All these areas now require the analysis and management of huge amounts of loosely structured data, and all need mathematical models to simulate phenomena and make predictions. Finally, about research institutes: Institutes and conference centers are important elements in the infrastructure supporting the mathematical sciences - as important as are lab facilities and observatories to physics and astronomers. The Institute for Advanced Study in Princeton, New Jersey, was the first institute to assemble, for short periods (4-12 months) groups of mathematical science researchers. Such institutes have become popular in the mathematical sciences and are viewed as making significant contributions to the advance of the discipline because they enable explorations of new developments, facilitate collaboration among mathematical scientists and assist in the sharing of ideas between mathematical scientists and those of other disciplines. 1.2 The national and international context In many countries, both within Europe and outside, there are Mathematical Research Centers, all based on the idea that investment in research, both basic and applied, is a fundamental component in the scientific and technological development of society. We mention just a few of them: in the United States, the Mathematical Science Research Institute of Berkeley, the Institute for Mathematics and its Applications at Minneapolis, the Center for Applied Mathematical Sciences in Los Angeles, and the Santa Fe Institute; in France, the IHES at Bures-sur-Yvette (Paris); in Germany, the two Max Planck Institutes at Bonn and Leipzig, and several Sonderforschungsbereiche in mathematics; in the United Kingdom, the Isaac Newton Institute at Cambridge, the Mathematical Research Center of the University of Warwick, and the International Centre for Mathematical Sciences in Edinburgh; in Sweden, the Mittag-Leffler Institute at Djursholm, Stockholm. In 1.3 we list the European Mathematical Centers grouped in ERCOM, the European Research Centres in Mathematics. Further, Canada has at least three centers; the Pacific Rim has several Mathematical Centers and is planning more; Australia has the Centre for Mathematics and its Applications at the Australian National University. Several centers have been and are being established in China and India. Each of the centers listed has its own character deriving from the diverse historical and scientific background of the host country. However, they all share a common aspect: to gather in one place for longer or shorter periods, scientists of various levels, to foster fruitful collaborations and to promote research in mathematics, both pure and applied. It is widely recognized that Pisa has played a role of great historical significance in the advance of mathematical science. Indeed, the names of Leonardo Pisano, called Fibonacci, and Galileo Galilei link it to the very origins of modern science. In years following the foundation of the Italian state, there emerged in Pisa a school of mathematics that reached the highest level of achievement with exponents such as Enrico Betti, Ulisse Dini, Luigi Bianchi, Enrico Bertini, Eugenio Elia Levi and Leonida Tonelli. With these beginnings the University and the Scuola Normale Superiore have progressively established Pisa as a true crossroad of international mathematical 8 Scientific and Administrative Report 2001_2005

8 research. Mathematical activity in Pisa underwent a renaissance in the second half of the 20 th century. For any mathematician recalling that era the names of Aldo Andreotti, Guido Stampacchia, Iacopo Barsotti, Edoardo Vesentini, Giovanni Prodi, Sergio Campanato and, certainly, Ennio De Giorgi come to mind as colleagues no longer teaching or no longer with us. It should also be remembered that, since the unification of Italy, a very high percentage of Italian mathematicians had their formation at the University of Pisa and, in particular, at the Scuola Normale. Moreover, an extremely high percentage of Italian mathematicians invited to give a presentation at the International Congress of Mathematicians (held every four years) had been or were professors at the Scuola Normale. The recent creation of the Scuola Superiore di Studi Avanzati Sant Anna has further enriched the Pisan intellectual landscape with new perspectives in applied research. Because of its long and prestigious tradition and because of the presence of a conspicuous number of internationally recognized mathematicians, Pisa is certainly one of the best suited cities in Italy to host a Research Center in Mathematics. 1.3 The Center The Research Center Ennio De Giorgi, Matematica nelle Scienze Naturali e Sociali was established at the end of 2001 as a center of the Scuola Normale Superiore, with the character of an inter-university center, by the three university institutions of Pisa: the University of Pisa, the Scuola di Studi Superiore Sant Anna and the Scuola Normale Superiore. The Center is located in Palazzo Puteano, former seat of the Collegio Puteano. The Collegio was founded in 1604 by Carlo Antonio Dal Pozzo, Archibishop of Pisa, who obtained the palace on perpetual lease from the Order of Santo Stefano. Recently the Fondazione Collegio Puteano headed by the Rector of the University of Pisa, has entrusted the Scuola Normale Superiore with the palace. The palace is an integral part of the Piazza dei Cavalieri, which was designed by Giorgio Vasari in 1561 for Cosimo I Medici, and it has recently been restored and renovated by the Scuola Normale Superiore under the direction of the architect Albertino Linciano. The Center has a Council, composed of two professors from the Scuola Normale, two professors from the University, and one professor from the Scuola Sant Anna, these members being named by the director and rector of the respective institutions. For the period the Council was composed of: Giovanni Dosi as representative of the Scuola Sant Anna, Franco Flandoli (who replaced Maurizio Pratelli in 2003) and Margherita Galbiati as representatives of the University of Pisa, Mariano Giaquinta and Giuseppe Tomassini as representatives of the Scuola Normale Superiore. The Center has a Scientific Committee, composed of five to eight scientists of international reputation, these being named jointly by the Director of the Scuola Normale, the Rector of the University of Pisa, and the Director of the Scuola Sant Anna. From the beginning the Committee has consisted of Jean Pierre Bourguignon (IHES, Buressur-Yvette), Luis Caffarelli (University of Texas, Austin), Stefan Hildebrandt (University of Bonn), Alan Kirman (Groupement de Recherche en Economie Quantitative, Marseille), Richard Schoen (Stanford University) and Jean-Christophe Yoccoz (Collège de France, Paris). The Center has a Director named by the Director of the Scuola Normale, in consultation with the Rector of the 9 Scientific and Administrative Report 2001_2005

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10 University and the Director of the Scuola Sant Anna. From the outset the director has been Mariano Giaquinta. The Center is named after Ennio De Giorgi, who was one of the most prominent figures in the renaissance of mathematics in Pisa in the second half of the last century. Ennio De Giorgi was one of the great mathematicians of the last century. Born in Lecce in 1928, he moved to Rome where he obtained a university degree in mathematics. At an early age he won a competition for a professorship in mathematics and, after a brief stay in Messina, was called to the Scuola Normale in He remained in Pisa until his death, on October 25, De Giorgi left a profound stamp on contemporary mathematics, in many aspects: in the problems he resolved, in the theories he elaborated, and in the large number of students he launched in research. He is noted for having resolved one of the problems formulated by David Hilbert in the early 1900 s, for his contributions to the theory of minimal surfaces, and for having developed, in the 1970 s, the very innovative theory of Gamma convergence, which provides a setting to unify many phenomena in mathematics and physics. Since 2003 the Center has been part of ERCOM (European Research Centres on Mathematics).The list of European Centers with representation in ERCOM, as approved by the European Mathematical Society Committee, includes Stefan Banach International Mathematical Center, Warsaw, Poland Centro Internacional de Matematica, Coimbra, Portugal Centre International de Rencontres Mathematiques, Luminy, France Centre de Recerca Matematica, Bellaterra, Spain Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands Emmy Noether Research Institute for Mathematics, Ramat-Gan, Israel Erwing Schroedinger International Institute for Mathematical Physics, Wien, Austria Euler International Mathematical Institute, St. Petersburg, Russia European Institute for Statistics, Probability and Operation Research, Eindhoven, The Netherlands International Centre for Mathematical Sciences, Edinburgh, United Kindom The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy Institut des Hautes Etudes Scientifiques, Bures-Sur-Yvette, France Institut Henri Poincaré, Centre Emile Borel, Paris, France Institut Mittag-Leffler, Djursholm, Sweden Istituto Nazionale di Alta Matematica, Roma, Italy Isaac Newton Institute for Mathematical Sciences, Cambridge, United Kingdom Lorenz Center, Leiden, The Netherlands Centre for Mathematical Physics and Stochastics, Aarhus, Denmark Mathematisches Forschungsinstitut Oberwolfach, Germany Max Planck Institute for Mathematics in Sciences, Leipzig, Germany Max Planck Institute for Mathematics, Bonn, Germany, Mathematical Research Institute, Nijmegen, The Netherlands Thomas Stieltjes Institute for Mathematics, Leiden, The Netherlands The Center has also established agreements for academic collaboration with several prestigious institutions. The list includes: Center for Applied Mathematical Sciences, University of Southern California, Los Angeles Center for Mathematics and its Applications, Australian National University, Canberra Centre d Analyse et de Mathématique Sociale, Ecole des Hautes Etudes en Sciences Sociales, Paris Department of Mathematics, ETH, Zürich Faculty of Mathematics and Physics Charles University, Prague Graduate School, Nanjing University of Science and Technology Institute for Mathematics, Academia Sinica, Taiwan Institut Mittag-Leffler, Djursholm, Sweden Instituto Nacional de Matematica Pura e Aplicada, IMPA, Rio de Janeiro Institute of Mathematical Sciences of Waseda University, Japan 11 Scientific and Administrative Report 2001_2005

11 Mathematics Research Center, University of Warwick Sonderforschungsbereich 611, University of Bonn Stefan Banach International Mathematical Center Finally, the Center acknowledges support from the following institutions: Scuola Normale Superiore, Pisa Università di Pisa Scuola Superiore Sant Anna, Pisa Università di Lecce Università di Trento MIUR, Ministero per l Istruzione, l Università e la Ricerca MIUR research funds Unione Matematica Italiana Istituto Nazionale di Alta Matematica Gruppo Nazionale per l Analisi Matematica la Probabilità e le loro Applicazioni Consorzio Interuniversitario per l Alta Formazione in Matematica Comune di Lizzanello, Italy Fondazione Cassa di Risparmio di Lucca Springer Verlag, Berlin Birkhäuser Verlag, Basel The Center has two non-permanent administrative positions presently occupied by: Dr. Ilaria Gabbani and Dr. Antonella Gregorace. 1.4 Aims of the Center The Center intends to: gather Italian and foreign researchers, both junior and senior, with the idea of fostering collaboration and exchange of ideas, producing researchers specializing in interdisciplinary endeavours, organize periods of several months during which there will be a focus on a research area of particular relevance, including pure mathematics and applications in the natural and social sciences, e.g. physics, biology, finance and economics. These periods of specialization will bring together Italian and foreign scientists and will also provide an environment for the training of researchers coming from developing countries, promote new ideas and research at the frontiers of interdisciplinary studies, promote the formation of collaborative research nuclei from among those present, to advance particular areas of mathematics, its application to the natural and social sciences, and its application to problems in the industrial and technological arena. The Center intends also to contribute to the cultural mathematical formation of teachers and laymen; in fact, while for centuries some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person, nowadays, when mathematics pervades both science and technology more than ever, mathematical awareness seems lacking. 12 Scientific and Administrative Report 2001_2005

12 1.5 The Agreement This is the text of the agreement among the Scuola Normale Superiore, the University of Pisa, and the Scuola Superiore Sant Anna signed on November 20, 2001: CONVENZIONE TRA SCUOLA NORMALE SUPERIORE DI PISA, UNIVERSITÀ DI PISA, SCUOLA SUPERIORE DI STUDI UNIVERSITARI E DI PERFEZIONAMENTO SANT ANNA DI PISA Premessi e considerati: la prestigiosa tradizione scientifica degli studi matematici nelle istituzioni universitarie pisane e il ruolo particolare nella crescita della ricerca matematica a Pisa avuto dal prof. Ennio De Giorgi; l obiettivo della convenzione fra l Università di Pisa e la Scuola Normale Superiore sul Progetto MAP- Matematica a Pisa firmata nel 1992 e rinnovata nel 1997, di cui si allega il testo; il protocollo d intesa con cui le tre istituzioni si impegnano a istituire il Centro di Ricerca Matematica Ennio De Giorgi con le ragioni e finalità scientifiche in allegato; l interesse, non solo locale ma nazionale e internazionale, che si costituisca a Pisa, in accordo tra le tre istituzioni pisane, un centro di eccellenza per la ricerca matematica, anche di carattere applicativo e interdisciplinare; si conviene e si stipula quanto segue: Art.1 È istituito il Centro di Ricerca Matematica Ennio De Giorgi, Matematica nelle Scienze Naturali e Sociali. Il Centro ha le seguenti finalità: ospita e promuove progetti di ricerca di alto contenuto innovativo focalizzati sulla matematica sia pura che applicata alle scienze sociali e naturali, come pure sulle sue applicazioni industriali e tecnologiche; accoglie studiosi italiani e stranieri, sia junior che senior, con l intento di favorire le varie forme di collaborazione e la costituzione di masse critiche di ricercatori in specifiche aree di ricerca, soprattutto interdisciplinari; promuove la costituzione al suo interno di centri di eccellenza per la ricerca su tematiche specifiche della matematica e delle sue applicazioni alle scienze sociali e naturali. Art.2 La Scuola Normale Superiore mette a disposizione, quale sede logistica del Centro, il Collegio Puteano nella parte non destinato a foresteria della Scuola. Le altre due istituzioni collaborano al buon funzionamento delle attività del Centro, anche mettendo a disposizione temporaneamente risorse logistiche per le attività del Centro. Art.3 Il Centro ha la natura di centro interuniversitario, ha sede amministrativa presso la Scuola Normale Superiore ed è gestito da questa. I finanziamenti affluiscono alla Scuola Normale Superiore e sono gestiti secondo il regolamento amministrativo-contabile della Scuola Normale Superiore, nei limiti delle risorse finanziarie disponibili per il Centro. Art.4 Il finanziamento ordinario del Centro è garantito dai seguenti contributi: Euro per il 2001, Euro per il 2002, ed Euro per ciascuno degli anni 2003, 2004, 2005 da parte della Scuola Normale; Euro per il 2001, Euro per il 2002, ed Euro per ciascuno degli anni 2003, 2004, 2005 da parte dell Università di Pisa; Euro per il 2001, Euro per il 2002, ed Euro per ciascuno degli anni 2003, 2004, 2005 da parte della Scuola Sant Anna. Art.5 Il Consiglio del Centro è formato da due docenti della Scuola Normale, da due docenti della Università di Pisa e da un docente della Scuola Sant Anna, nominati dai rispettivi direttori e rettore. Il Consiglio sulla base dei pareri e dei suggerimenti del Comitato Scientifico, formula i piani annuali e pluriennali di attività del Centro ed i relativi bilanci preventivi e consuntivi. Art.6 Il Direttore del Centro è nominato dal Direttore della Scuola Normale tra i componenti del Consiglio del Centro, sentiti il Rettore dell Università di Pisa e il Direttore della Scuola Sant Anna. Resta in carica per cinque anni ed è rinnovabile. 13 Scientific and Administrative Report 2001_2005

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14 Art.7 Il Comitato Scientifico del Centro è formato da 5 a 8 personalità scientifiche nazionali e internazionali, nominati congiuntamente dal Direttore della Scuola Normale, dal Rettore dell Università di Pisa e dal Direttore della Scuola Sant Anna. All atto della nomina è specificata la durata del mandato comunque non superiore a cinque anni. Il Comitato Scientifico esprime pareri, proposte e suggerimenti al fine della formulazione dei piani annuali e pluriennali di attività e dell elaborazione delle proposte di bilancio del Centro. Esso ha inoltre il compito della valutazioni scientifica dell attività del Centro. Art.8 La presente convenzione ha durata fino al 31 dicembre 2005 e può essere rinnovata di ulteriori 5 anni sulla base di apposito atto aggiuntivo. Per quanto non espressamente previsto dalla presente convenzione, si fa riferimento allo Statuto e ai regolamenti della Scuola Normale Superiore. The activities of the year 2002 Since the Palazzo Puteano, seat of the Center, was not available for most of the year 2002, the activity of the Center was limited to organizing only two intensive research periods: Research Trimester on Dynamical Systems, February 4 - April 26, 2002 Scientific Committee: Stefano Marmi (Università di Udine and Scuola Normale Superiore), John Mather (Princeton University), John Milnor (Stony Brook University), Jacob Palis (IMPA, Rio de Janeiro), Jean-Christoph Yoccoz (Collège de France). Organizing Committee: Giuseppe Da Prato and Mariano Giaquinta (Scuola Normale Superiore, Pisa), and Stefano Marmi (Università di Udine and Scuola Normale Superiore, Pisa). Topics included: Holomorphic dynamics and foliations, small divisor problem, celestial mechanics, ergodic theory and randomly perturbed systems, periodic orbits and zeta functions, partially hyperbolic systems, bifurcation theory and related topics, and dynamics on non-archimedean fields. The list of speakers included: V. Baladi (IHES, Bures-sur-Yvette), J. Bochi (IMPA, Rio de Janeiro), J. Buzzi (Ecole Polytechnique, Palaiseau), A. Chenciner (Université Paris 7), L. Chierchia (Università di Roma Tre), A. De Melo (Collège de France), D. Dolgopyat (Pennsylvania State University), C. Favre (Université Paris 7), B. Fayad (Université Paris 13), G. Forni (Northwerstern University), J. Gerver (Rutgers University), A. Giorgilli (Università di Milano-Bicocca), V. Kaloshin (M.I.T.), Y. Kifer (Hebrew University), R. Krikorian (Ecole Polytechnique, Palaiseau), J. Laskar (CNRS), P. Le Calvez (Université Paris 13), S. Luzzatto (Imperial College, London), S. Marmi (Università di Udine e Scuola Normale Superiore, Pisa), J. Mather (Princeton University), J. Milnor (Stony Brook University), C.G. Moreira (IMPA, Rio de Janeiro), P. Moussa (CEA/Saclay), J. Palis (IMPA, Rio de Janeiro), J. Riveira (Stony Brook University), D. Sauzin (CNRS), L. Stolovitch (Laboratoire Emile Picard, Toulouse), M. Viana (IMPA, Rio de Janeiro), and J-C. Yoccoz (Collège de France). About 80 junior participants from 16 countries attended the various activities of the trimester. Among them 27 received a grant partially covering travel and living expenses. The trimester was partially supported by the Istituto Nazionale di Alta Matematica, within the program Bimestri e trimestri intensivi di ricerca, and by the European Science Foundation, within the program Prodyn. About 30 courses were held, each lasting from 3 to 10 hours; moreover, about 20 lectures were presented by invited participants. 15 Scientific and Administrative Report 2001_2005

15 Financial Markets: Mathematical, Statistical and Economic Analysis, April 29 - July 15, The activities of the year 2003 Scientific Committee: William Brock (University of Wisconsin- Madison), Darrel Duffie (Stanford University), Paul Embrechts (ETH, Zürich), Doyne Farmer (Santa Fe Institute), Hans Föllmer (Humboldt Universität, Berlin). Organizing Committee: Giuseppe Da Prato and Mariano Giaquinta (Scuola Normale Superiore, Pisa), Paolo Guasoni and Maurizio Pratelli (Università di Pisa), and Giuliano Bottazzi and Giovanni Dosi (Scuola Superiore di Studi Universitari e di Perfezionamento Sant Anna, Pisa). About 15 courses were held, each lasting from 3 to 10 hours; moreover, about 12 lectures were presented by young invited participants. Covered broad areas included: Derivative pricing and hedging in incomplete markets, term structure models, risk management, modelling dependence in finance, time series analysis, artificial markets, aggregation and aspects of behaviour finance. In the year 2003 the Center organized three intensive research bimesters and a one-month intensive period of research. Interacting Particles and Computational Biology, January 10 - March 10, 2003 Scientific Committee: Jean-Louis Deneubourg (Université de Bruxelles), Yuri Manin (Max-Planck Institut, Bonn) Hans Meinhardt (Max-Planck Institut, Tübingen), Philippe Mathieu (Institut Solvay Bruxelles), and Franco Flandoli (Università di Pisa). Organizing Committee: Franco Flandoli (Università di Pisa), Mariano Giaquinta and Giuseppe Tomassini (Scuola Normale Superiore, Pisa), and Philippe Mathieu (Insitut Solvay, Bruxelles). About 14 courses were held, each lasting from 2 to 8 hours; moreover 16 (research and tutorial) lectures were given by the participants. The list of speakers included: Topics included: K. Back (Washington University), M. Dacorogna (Converium Ltd), D. Duffie, C. Hommes (Amsterdam University), Y. Kabanov (Université de Franche-Comté, Besançon), D. Madan (University of Maryland), A. McNeil (ETH, Zürich), T. Mikosch (Copenhagen University), M. Pagano (Università di Salerno), K. Singleton (Stanford University), S. Skouras (Santa Fe Institute), and N. Touzi (Centre de Recherche en Économie et Statistique). About 80 junior participants from 16 countries attended the various activities of the trimester. Among them 17 received a grant partially covering travel and living expenses. The trimester was partially supported by the Department of Mathematics of the University of Pisa and by the Scuola Sant Anna. Moreover Darrel Duffie gave the Lezioni Galileiane of the Scuola Normale, supported by the Amici della Scuola Normale. Collective behaviour in biological systems, self-organization and patterns formation arising from local interactions, specific biological systems from molecular biology and animal societies, and topics from sciences of complexity. The list of speakers included: T. Aubin (CNRS, Paris), V. Capasso (Università di Milano), A. Carbone (IHES, Bures-sur-Yvette), J. P. Crutchfield (Santa Fe Institute), F. Cuker (Hong Kong University), P. De Kepper (CNRS Bordeaux), J. D. Deuschel (Technischen Universität, Berlin), M. Giacca (Scuola Normale Superiore, Pisa), G. Giacomin (Université Paris 7), M. Isopi (Università di Bari and New York University) P. Malliavin (Université Paris 6), A. Martinoli (California Institute of Technology), H. Meinhardt (Max-Planck Institut), R. Turner (University of Wisconsin-Madison), and T. Vicsek (University of Budapest). 16 Scientific and Administrative Report 2001_2005

16 About 60 participants attended the various activities of the bimester. Among them 20 received a grant partially covering travel and expenses. The bimester was partially supported by the Department of Applied Mathematics of the University of Pisa. Topics in Complex and Real Geometry, March 15 - May 15, 2003 Scientific Committee: Jean-Pierre D ly (Université de Grenoble), Janos Kollar (Princeton University), Adam Parusinski (Université de Angers), Alberto Tognoli (Università di Trento), Giuseppe Tomassini (Scuola Normale Superiore, Pisa). Organizing Committee: Fabrizio Broglia (Università di Pisa), Giuseppe Tomassini (Scuola Normale Superiore, Pisa). About 15 mini-courses and more than 50 talks were held. During the bimester a special session of the annual meeting of the European Group of Real Algebraic and Analytic Geometry took place. Covered areas included: Subanalytic geometry, global analytic sets, nash functions and manifolds, real algebraic varieties and maps, analytic vector fiels, three manifolds and symplectic and hyperbolic geometry, complex analysis in infinite dimensions, noncritical holomorphic functions on Stein manifolds, constructive hyperbolicity, complex geometry of orbits, geometry of positive cones in compact Kähler manifolds, CR geometry, approximate solutions and Poletsky theory of disks, functional spaces of holomorphic functions, group action on complex manifolds, the Levi problem, symplectic, Kähler and algebraic geometry. The list of speakers included: Carlos Andradas (Universidad Complutense Madrid), Daniel Barlet (Institut Elie Cartan, Nancy), Bo Berndtsson (Chalmers University of Technology, Göteborg), Andreas Bernig (University of Münster), Edward Bierstone (University of Toronto), Jacek Bochnak (University of Amsterdam), Isabelle Bonnard (Université de Angers), Anne-Marie Chollet (Université Lille 1), Michel Coste (Université de Rennes 1), Jean-Pierre D ly (Université de Grenoble), Klas Diederich (Wuppertal University), Julien Duval (Laboratoire Picard, Toulouse), Peter Ebenfelt (Royal Institute of Technology, Stockholm), Abdelhafed Elkhadiri (Université de Kenitra, Maroc), Franc Forstneric (University of Ljubliana), Jean-Pierre Françoise (Université Paris 6), Andrei Gabrielov (Purdue University), Isabelle Gondard (Ruhr-Universität Bochum), Alan Huckleberry (Ruhr-Universität Bochum), Johannes Huisman (Université de Rennes 1), Ilia Itenberg (Université de Rennes 1), Mattias Jonsson (Michigan State University), Burglind Jöricke (Uppsala Universitet), Viatcheslav Kharlamov (IRMA, Strasbourg), Siegmund Kosarew (Institut Fourier, Grenoble), Krzysztof Kurdyka (Université de Savoie), Christine Laurent (Institut Fourier, Grenoble), Jürgen Leiterer (Humboldt-Universität, Berlin), Laszlo Lempert (Purdue University), Jean-Marie Lion (Unversité de Rennes 1), George Marinescu (Humboldt-Universität, Berlin), Clint McCrory (University of Georgia), Grigory Mikhalkin (University of Utah), Takeo Ohsawa (Nagoya University), Adam Parusinski (Université de Angers), Alexander Prestel (Universität Konstanz), Jean-Pierre Rosay (University of Wisconsin- Madison), Bernard Shiffman (Johns Hopkins University), Nikolay Shcherbina (Chalmers University of Technology, Göteborg), Masahiro Shiota (Nagoya University), Nessim Sibony (Université Paris-Sud 11), and Alexander Tumanov (University of Illinois). More than 200 people participated in the activities of the bimester. Partial support was provided by the Scuola Normale Superiore and by the departments of Mathematics of Pisa and of Trento via PRIN funds. Supports were also provided by the European Group of Real Algebraic and Analytic Geometry. Probability and Statistical Mechanics in Information Science, May 20 - July 20, 2003 Scientific Committee: Sanjoy Mitter (M.I.T.), Giorgio Parisi (Università di Roma La Sapienza ), and S. R. Srinivasa Varadhan (Courant Institute, New York ). Organizing Committee: Sergio Caracciolo (Università di Milano), Fabio Fagnani (Politecnico di Torino), Franco Flandoli 17 Scientific and Administrative Report 2001_2005

17 18 Scientific and Administrative Report 2001_2005

18 (Università di Pisa), and Andrea Mennucci (Scuola Normale Superiore). About 30 short series of courses were held. Several short talks were given by the participants. Covered broad areas included: Probabilistic results in statistical mechanics and information theory; quantum information; algorithms in statisitical physics, combinatorial optimization and error correcting codes in information theory; information theory, nonequilibrium mechanics and disordered systems; percolation and related models; scaling limits, and network information theory. The list of speakers included: Luigi Accardi (Università di Roma Tor Vergata ), Claudio Altafini (Scuola Internazionale Superiore di Studi Avanzati, Trieste), Gérard Ben Arous (Courant Institute, New York), Ugo Boscain (SISSA Trieste), Pierluigi Cantucci (Università di Bologna), Carlo Cosmelli (Università di Roma La Sapienza ), Paolo Dai Pra (Università di Padova), Bertrand Duplantier (CEA/Saclay), Nicola Elia (Iowa State University), Fabio Fagnani (Politecnico di Torino), Franco Fagnola (Università di Genova), G. David Forney (M.I.T.), Massimo Franceschetti (University of California, Berkeley), Alberto Gandolfi (Università di Milano-Bicocca), Paolo Gibilisco (Università di Chieti), Francesco Guerra (Università di Roma La Sapienza ), Marco Isopi (Università di Bari & New York University), Giovanni Jona- Lasinio (Università di Roma La Sapienza ), Panganamala Ramana Kumar (University of Illinois), Andrea Montanari (Ecole Normale Supérieure), Ronald Meester (University of Amsterdam), Nigel Newton (University of Essex), Michele Pavon (Università di Padova), Matteo G A Paris (Università di Pavia), Giorgio Parisi (Università di Roma La Sapienza ), Balaji Prabhakar (Stanford University), Fraydoun Rezakhanlou (University of Berkeley), Rahul Roy (Indian Statistical Institute), Nicolas Sourlas (Ecole Normale Supérieure), Sekhar Tatikonda (Yale University), I. Emre Telatar (Ecole Polytechnique Fédérale de Lausanne), Boris Tsirelson (University of Tel Aviv), Ruediger Urbanke (Ecole Polytechnique Fédérale de Lausanne), S.R.S. Varadhan (Courant Institute, New York), Pascal Olivier Vontobel (University of Illinois, Urbana-Champaign), Martin Wainwright (University of California, Berkeley), Riccardo Zecchina (International Centre for Theoretical Physics, Trieste), and Ofer Zeitouni (University of Minnesota). About 100 people participated in the activity of the bimester, most of them received partial support for their living expenses. Partial supports were provided by the Scuola Normale Superiore, Pisa, the Department of Applied Mathematics in Pisa, the Departments of Physics in Milano and of Informatics in Verona, and by GNAMPA. Moreover, S. R. Varadhan held the Cattedra Galileana, supported by the Amici della Scuola Normale, and gave 16 onehour lectures on Large deviations and Exclusive processes. In September, in collaboration and with the partial support of the European Group on Harmonic Analysis, the Center organized a Summer School in Harmonic Analysis, September 1-13, 2003 Scientific Committee: Aline Bonami (Université d Orléans), Marco Peloso (Politecnico di Torino), and Fulvio Ricci (Scuola Normale Superiore, Pisa). Six series of six-hours lectures were given by J. P. Anker (Université d Orléans), A. Nagel (University of Wisconsin-Madison), A. Volberg (Michigan State University), A. Carbery (University of Edinburgh), E. Damek (Wroclaw University), and L. Vega (Universidad del Pais Vasco). More than 70 people attended the school, 30 of them were partially supported. Partial support was also provided by GNAMPA. Intensive Research Period on Geometric Analysis, November 1-30, 2003 Scientific Committee: G. Alberti (Università di Pisa), M. Giaquinta, and C. Mantegazza (Scuola Normale Superiore, Pisa). 19 Scientific and Administrative Report 2001_2005

19 The aim of the activity was to bring together researchers of different universities and encourage informal exchanges of ideas on Geometric Analysis in general and, in particular, on geometric variational problems. More than 28 talks were held. The list of participants included: Luis Almeida (Université de Nice Sophia-Antipolis), Sisto Baldo (Università di Trento), Giovanni Bellettini (Università di Roma Tor Vergata ), Fabrice Bethuel (Université Paris 6), Xavier Cabré (Universitat de Barcelona), Camillo De Lellis (ETH, Zürich), Olivier Druet (Ecole Normale Supérieure, Lyon), James Eells (Warwick University), Adriana Garroni (Università di Roma La Sapienza ), Qing Han (University of Notre Dame, Indiana), Emmanuel Hebey (Université de Cergy-Pontoise), Frederic Helein (Université Paris 7), Stefan Hildebrandt (Universität Bonn), David Holcman (San Francisco), Min-chun Hong (University of New England, Armidale), Ernst Kuwert (Freiburg Universität), Giuseppe Modica (Università di Firenze), Domenico Mucci (Università di Parma), Matteo Novaga (Università di Pisa), Giandomenico Orlandi (Università di Verona), Frank Pacard (Université Paris 12), Emanuele Paolini (Università di Firenze), Adriano Pisante (Università di Roma La Sapienza ), Maria Alessandra Ragusa (Università di Catania), Etienne Sandier (Université Paris 12), Reiner Schaetzle (Universität Bonn), Carlo Sinestrari (Università di Roma Tor Vergata ), Didier Smets (Université Paris 6), Sergio Solimini (Politecnico di Bari), Jiri Soucek (Charles University, Praha), Pavel Strzelecki (Wroclaw University), Michael Struwe (ETH, Zürich), Atsushi Tachikawa (Noda), Ali Taheri (Warwick University), Gabriella Tarantello (Università di Roma Tor Vergata ), Yoshihiro Tonegawa (Hokkaido University), Peter Topping (Warwick University), Neil Trudinger (ANU, Canberra), Nina Uraltseva (St. Petersburg State University), and Yang Xiaoping (Nanjing University). About 60 people participated in the activities. The period was partially supported from research funds at the Scuola Normale Superiore. The Center, with the scientific collaboration of Giuseppe Da Prato (Scuola Normale Superiore, Pisa), organized the following workshop: Two days on Kolmogorov Equations, October 17-18, 2003 Lectures were given by: P. Acquistapace (Università di Pisa), V. Barbu (Iasi, Romania), M. Bertoli (Università di Parma), S. Bonaccorsi (Università di Trento), S. Cerrai (Università di Firenze), D. Di Giorgio (Università di Parma), F. Flandoli (Università di Pisa), S. Fornaro (Università di Lecce), M. Fuhrman (Università di Milano), F. Gozzi (Università di Roma), G. Guatteri (Milano), L. Lorenzi (Università di Parma), A. Lunardi (Università di Parma), S. Mazzucchi (Università di Trento), G. Metafune (Università di Lecce), D. Pallara (Università di Lecce), E. Priola (Università di Torino), M. Roeckner (Universiaet Bielefeld), R. Stasi (Università di Pisa), G. Tessitore (Università di Parma), and L. Zambotti (Università di Pisa). Further, the Center hosted or/and partially supported the following workshops: HYTEC-1 The hybrid organic-inorganic heterostructures for photonics and telecommunications, Pisa, April 2, 2003, Cantor e Dedekind: uno straordinario incontro di idee. Letture a due voci tratte dall epistolario, Viareggio, September 4-6, 2003, Optimal transport theory and applications, Pisa, October 9-12, 2003, Case studies in Industrial Mathematics, December 19-20, Distinguished senior visitors Thanks to supports received from the Unione Matematica Italiana and from the Fondazione Cassa di Risparmio di Lucca, in 2003 the Center began a program of short-term distinguished visitors. UMI Lecturer 2003: Frédéric Helein (Ecole Normale Supérieure de Cachan), November Pieri Visitor: Neil Trudinger (Australian National University), November Scientific and Administrative Report 2001_2005

20 Research nucleus In 2003 a research nucleus on Holomorphic Dynamical systems and Arithmetic, formed by M. Abate and C. Carminati (Università di Pisa) and S. Marmi (Scuola Normale Superiore, Pisa) began its activity at the Center. 1.8 The activities of the year 2004 In the year 2004 the Center organized two intensive research trimesters and one bimester. Phase Space Analysis of Partial Differential Equations, February 15 - May 15, 2004 Public Lectures: Matematica, Cultura e Società In 2003 the Center started a program of public lectures. Seven lectures were given by: Scientific Committee: Jean-Michel Bony (Ecole Polytechnique, Paris), Ferruccio Colombini (Università di Pisa), Sergiu Klainerman (Princeton University), Nicolas Lerner (Université de Rennes 1), and Francois Treves (Rutgers University). Enrico Giusti (Università di Firenze), Piero Villaggio (Università di Pisa), Luciano Modica (Università di Pisa), Piergiorgio Odifreddi (Università di Torino), Lucio Russo (Università di Roma Tor Vergata ), Benedetto Scimemi (Università di Padova), and Stefan Hildebrandt (Universität Bonn). Each lecture was attended by more than 70 people, ranging from high-school students and teachers, to university students and professors, and to laymen. Follow-up Courses The Center organized also three one-week follow-up courses for teachers with the collaboration of Franco Conti (Scuola Normale Superiore, Pisa) and with the goal of communicating some non-trivial mathematics: Franco Conti (Scuola Normale Superiore, Pisa), Le Curve celebri, October 2003, Fulvio Ricci (Scuola Normale Superiore, Pisa), Matematica e tomografia, November 2003, Stefano Marmi (Scuola Normale Superiore, Pisa), Iterazioni, attrattori e caos, Dicembre Unfortunately the first course could not take place because of the premature death of Franco Conti. Topics included: Pseudodifferential calculus (in its Weyl formulation) and its refinements based on Littlewood-Paley decompositions; paradifferential operators, extending pseudodifferential operators to nonlinear equations, allowing a deep analysis of the singularities of their solutions; Fourier integral operators and the WKB methods of linear, as well as nonlinear, geometrical optics and their connections with symplectic geometry; Strichartz inequalities, iterative methods to solutions of nonlinear PDE, the study of the local L p regularity of solutions - mainly of hyperbolic and Schrödinger-type equations. The list of speakers included: S. Alinhac (Université Paris-Sud 11), J.-M. Bony (Ecole Polytechnique), A. Bove (Università di Bologna), J.-Y. Chemin (Ecole Polytechnique), P.D. Cordaro (University of San Paulo, Brazil), P. D Ancona (Unversità di Roma La Sapienza ), D. Del Santo (Università di Trieste), N. Dencker (Lund University), C. Fefferman (Princeton University), V. Georgiev (Università di Pisa), P. Gérard (Université Paris- Sud 11), D. Jerison (M.I.T.), L. Hörmander (Lund University), K. Kajitani (Tsukuba University), S. Klainerman (Princeton University), J. Krieger (Harvard University), W. Matsumoto (Ryukoku University), G. Métivier (Université Bordeaux 1), T. Nishitani (Osaka University), A. Parmeggiani (Università di Bologna), L. Pernazza (Università di Pavia), V. Petkov (Université Bordeaux 1), J. Rauch (University of Michigan, Ann Arbor), I. Rodnianski (Princeton University), T. Sideris 21 Scientific and Administrative Report 2001_2005

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