INSTITUT MITTAG-LEFLER – A NORDIC INSTITUT FOR RESEARCH IN MATHEMATICS Activity report Institut Mittag-Leffler is a Nordic research institute for mathematics. It was founded in 1916 by Professor Gösta Mittag-Leffler and his wife Signe, who donated their magnificent villa with its first-class library for the purpose of creating the Institute that bears their name. The Institute is today an active international center for front-line research in the mathematical sciences, operating under the auspices of the Royal Swedish Academy of Sciences. It enjoys the economic support of national funding agencies from all the Nordic countries, as well as of some private foundations. The main activities at the Institute are the research programs and the publication of two research journals. The Institute conducts semester-long programs aimed at research in some area in pure or applied mathematics of current interest. The ambition is that over time all areas of current interest to mathematicians in the Nordic countries are served. The programs during the current 10-year period – past, present and future – are: • Probability and conformal mappings, fall 2001 and spring 2002. • Partial differential equations and spectral theory, fall 2002. • Mathematical control and systems theory, spring 2003. • Noncommutative geometry, fall 2003 and spring 2004. • Queuing theory and teletraffic theory, fall 2004. • Algebraic combinatorics, spring 2005. • Wave motion, fall 2005. • Algebraic topology, spring 2006. • Moduli spaces, fall 2006 and spring of 2007. • Stochastic partial differential equations, fall 2007. • Several complex variables, spring 2008. • Geometry, analysis, and general relativity, fall 2008. • Discrete probability, spring 2009. • Mathematical logic: Set theory and model theory, fall 2009. • Dynamical systems and PDEs, spring 2010. • Quantum information theory, fall 2010. • Algebraic geometry with a view to applications, spring 2011 • Complex analysis and integrable systems, fall 2011. • Geometric and analytic aspects of group theory, spring 2012. The subject area for each research program is decided circa 2 1/2 years in advance by the board of the Institute, based on submitted proposals. An international evaluation committee is appointed, which meets at the Institute and conducts interviews with the prospective organizers as a basis for the recommendations submitted to the board. Each research program is led by an organizing committee. Based on the recommendations of this committee the Institute invites senior and junior mathematicians to come and work together at the Institute. The senior participants are chosen among the internationally leading mathematicians in the given area. To the junior 1 INSTITUT MITTAG-LEFLER – A NORDIC INSTITUT FOR RESEARCH IN MATHEMATICS participants, typically recent Ph.D.s, we offer fellowships, open to everyone to apply for. Mathematicians from the Nordic countries are given a slight priority, however we make sure that scientific caliber and a good mixture of talents and backgrounds have top priority, to optimize the creative environment at the Institute. During 2009 there were a total of 151 visiting researchers, working a total of 272.5 man- months at the Institute as part of the following programs: Discrete Probability, spring of 2009 Organizing committee: Sven Erick Alm, Uppslala Olle Häggström, CTH, Göteborg Svante Janson, Uppsala Kurt Johansson, KTH, Stockholm Jeff Steif, CTH, Göteborg Mathematical Logic: Set Theory, fall of 2009 Organizing committee: Dag Normann, Oslo Erik Palmgren, Uppsala Jouko Väänänen, Amsterdam and Helsinki Hugh Woodin, Berkeley Detailed reports and documentation on these programs can be found later in this annual report. The research programs are conducted in a way that recognizes the immense value of having the time and the freedom to follow one's research interests wherever developments lead rather than having to deliver on predetermined goals. For this reason we require of all participants that they stay at least one month, to ensure time for substantial work. An aspect of the programs that is emphasized is to provide good postdoctoral training to the junior participants. Special seminars and minicourses are given specifically for them. In addition to these area-specific research programs we have the RIP program (Research in Peace), which allows Nordic mathematicians to spend time at the Institute for independent research. The Institute publishes two journals, Acta Mathematica (founded in 1882) and Arkiv för matematik (founded in 1903). Information about the journals is given on page www.mittag- leffler.se/publications/. Acta Mathematica has won a standing as one of a handful of journals generally considered to be the most important ones among all mathematics research journals. Institut Mittag-Leffler is an active participant in international scientific life. In particular, it participates in international networks of research institutes in mathematics. For instance, we belong to ERCOM (European Research Centers on Mathematics), a network of European sister institutes. We also belong to EPDI (European Post-Doctoral Institute), a collaboration between 9 institutes for jointly awarding postdoctoral fellowships to Europe's most promising young mathematicians. During 13-14 March Institut Mittag-Leffler hosted the annual ERCOM meeting. 30 directors and administrators representing 21 of the 26 ERCOM member institutes met in Djursholm to discuss matters of common concern and to share information. 2 INSTITUT MITTAG-LEFLER – A NORDIC INSTITUT FOR RESEARCH IN MATHEMATICS Participants at the ERCOM meeting The efforts to improve the Institute's financial situation have led to some small progress during 2009. Being a Nordic institute, we benefit from contributions from all Nordic countries (including Iceland). On 22 September a Nordic meeting was held at the Institute to discuss its financial basis. Representatives from the national research councils of Denmark, Finland, Norway and Sweden were present, as well as mathematicians from these countries. The meeting indicated a general willingness from our neighboring countries to increase their contributions. Institut Mittag-Leffler extends its warm gratitude to all organizations and individuals who via grants and contributions of various kinds have made the work of the Institute possible during the year 2009. Anders Björner Director 3 INSTITUT MITTAG-LEFLER – A NORDIC INSTITUT FOR RESEARCH IN MATHEMATICS Contributors The Institute is very grateful to the following organizations and individuals for contributions and support during 2009: The Swedish Research Council (Vetenskapsrådet) Academy of Finland The Danish Research Councils The Icelandic Mathematical Society The Research Council of Norway Acta Mathematicas fond Barbro Osher Pro Suecia Foundation Department of Mathematics, University of Oslo European Science Foundation's Set theory Research Network INFTY program Fonden ”Till bröderna Jacob och Marcus Wallenbergs minne” Stiftelsen G.S. Magnusons fond The Anna-Greta and Holger Crafoord Fund 4 INSTITUT MITTAG-LEFLER – A NORDIC INSTITUT FOR RESEARCH IN MATHEMATICS Discrete Probability Scientific report 2009 spring The spring 2009 Mittag-Leffler programme on discrete probability saw intense work in the intended broad spectrum ranging from, on one hand, basic probabilistic objects such as Markov chains, random walks, random graphs and random matrices, to, on the other hand, applications in computer science, statistical mechanics and the modeling of epidemics and social networks. A central meeting point for the participants was the seminar taking place Tuesdays and Thursdays; a total of 74 seminars were delivered. The seminar was very lively and led (together with the frequent more informal discussions during coffee breaks, in corridors and in hallways) to several unexpected collaborations. Recurrent themes covered in the seminar from a variety of angles include, for instance, the Ising model, Poisson processes, sorting and selection algorithms, Gaussian unitary ensembles, percolation models including dynamical percolation, different aspects of random graphs, and random walks with various (self-)interactions or in random environments. There were a number of research projects completed in the area of percolation, particle systems and related topics. John Wierman, who participated the entire semester, showed in collaborative work that certain pairs of 2-dimensional lattices have the same critical exponents. Remco van der Hofstad succeeded in uncovering the structure of the size of the largest component for nonhomogeneous graphs; the critical quantity turns out to be the tail behavior of the degree. Jonathon Peterson and Timo Seppäläinen obtained very precise results concerning current fluctuations for a system of random walks moving in a common fixed random environment; it turns out that the fluctuations are occurring at two different scales. Maria Deijfen and Olle Häggström constructed an example of a percolation model where the speed of a biased random walk on the cluster is not monotone in the bias; this monotonicity is believed to hold for i.i.d. percolation. This example therefore shows that the i.i.d. assumption is critical. One important area studied during the program was random graphs. In particular, progress was made on several fronts in the study of inhomogeneous random graphs, with contributions in the form of completed preprints by Tom Britton, Maria Deijfen, Remco van der Hofstad, Svante Janson, Mathias Lindholm, Tomasz \Luczak,