Isaac Newton Institute for Mathematical Sciences Current and Future Programmes Summary and Listing of Past Programmes November 2008 On the advice of the Scientific Steering Committee, the following programmes have been confirmed to 2011:
Mathematics and Physics of Anderson Localization: 50 Years After 14 July to 19 December 2008 Organisers: Professor YV Fyodorov (Nottingham), Professor I Goldshied (Queen Mary, London), Professor T Spencer (Princeton) and Professor MR Zirnbauer (Cologne)
In his seminal paper Absence of diffusion in certain random lattices (1958) Philip W Anderson discovered one of the most striking quantum interference phenomena: particle localization due to disorder. Cited in 1977 for the Nobel prize in physics, that paper was fundamental for many subsequent developments in condensed matter theory. In particular, in the last 25 years the phenomenon of localization proved to be crucial for the understanding of the Quantum Hall effect, mesoscopic fluctuations in small conductors as well as some aspects of quantum chaotic behaviour.
The goal of the programme is to bring together the world leaders in spectral theory of random Schrödinger operators and theoretical physicists working on the problem of Anderson localization. Among the topics that will be addressed during the programme are: the nature of critical phenomena associated with localization-delocalization transitions; the existence and statistical properties of extended states for D > 2 and the behaviour in the critical dimension D = 2; rigorous version of supersymmetric methods and of the nonlinear σ−model techniques; the localization-delocalization phenomena associated with the Integer Quantum Hall effect; rigorous mathematical understanding of the relation between magnetic Schrödinger operators and network models, and the connection with quantum percolation; localization in the presence of a random magnetic field; behaviour of products of random matrices and associated Lyapunov exponents; localization and delocalization in disordered systems characterised by non-selfadjoint operators; dynamical localization in Quantum Chaotic systems; localization in systems with aperiodic potential, as well as in models with correlated or long-ranged disorder; localization in systems with nonlinearities, and localization- delocalization phenomena in disordered systems of interacting quantum particles.
The Nature of High Reynolds Number Turbulence 26 August to 19 December 2008 Organisers: Professor P Bartello (McGill), Dr PA Davidson (Cambridge), Professor D Dritschel (St Andrews), Professor Y Kaneda (Nagoya) and Professor R Kerswell (Bristol) Turbulence is a notoriously difficult subject. Our attempts to understand it tend to consist of an uneasy mix of plausible but uncertain hypotheses, deterministic but highly simplified cartoons, and vast, complex data sets. For the small scales in turbulence this mixture of hypothesis, theory and experiment is given some unity by the phenomenological picture established by Richardson, Taylor and Kolmogorov. This phenomenology paints a picture of cascades of energy and information from large-scale eddies down to small, and of universal features of these cascades, provided the Reynolds numbers is large enough. In some sense this vision has worked well, providing a convenient conceptual framework within which many empirical observations can be rationalised. However, it was clear from the outset that this was too simplistic a point of view and half a century later there remain many fundamental unanswered questions. For example, exactly what do we mean by an eddy or a cascade, and how should we interpret cascade-like arguments in terms of the evolving morphology of the vorticity field? Indeed, what is the spatial structure of the vorticity field and how does this relate to the observed energy spectra? Our understanding of turbulent boundary-layers, and of turbulence in rotating-stratified fluids, is equally uncertain. For example, the log-law of the wall represents an early milestone in turbulence theory. It is based on the hypothesis that the near-wall eddies are immune from the remote eddies in the core flow. However, we have always known that the near-wall eddies cannot be independent of the larger far-field vortices, so why does the log-law work so well? There are many other controversies in shear flows. For example, it has been known for over thirty years that turbulence near a wall is dominated by streaks of low-speed fluid and by long, stream-wise vortices. It is now generally agreed that these streaks and vortices interact in some kind of quasi-periodic cycle, yet the nature of this cycle, and its possible relationship to the structures seen in transition studies, is still a matter of debate.
The goal of this programme is to bring together leading experts from across the world to debate these fundamental questions. The discussion will be wide ranging, from the initiation of turbulence through to its asymptotic state at high Reynolds number, including the effects of rotation and stratification, and the addition of different phases, such as bubbles, particles and polymers.
Algebraic Lie Theory 12 January to 26 June 2009 Organisers: Professor M Geck (University of Aberdeen), Professor A Kleshchev (University of Oregon) and Professor G Röhrle (University of Southampton) Lie theory has profound connections to many areas of pure and applied mathematics and mathematical physics. In the 1950s, the original ‘analytic’ theory was extended so that it also makes sense over arbitrary algebraically closed fields, in particular, fields of positive characteristic. Understanding fundamental objects such as Lie algebras, quantum groups, reductive groups over finite or p-adic fields and Hecke algebras of various kinds, as well as their representation theory, are the central themes of ‘Algebraic Lie Theory’.
A driving force has always been the abundance of challenging, yet very basic problems, such as finding explicit character formulae for representations. The introduction of geometric methods (in the 1970s) revolutionized the field. It led to a flow of new ideas between several disciplines, and produced spectacular advances. The ideas of ‘geometrization’ and ‘categorification’ now play a fundamental role in the development of the subject. New structures continue to arise from connections with other areas of mathematics and mathematical physics, like the emerging theory of W-algebras.
It is anticipated that the activities of the programme will lead to a focalisation and popularisation of the various recent methods, advances and applications of Algebraic Lie Theory.
Discrete Integrable Systems 19 January to 3 July 2009 Organisers: Professor RG Halburd (University College London), Professor F W Nijhoff (Leeds), Professor M Noumi (Kobe), Professor G R W Quispel (La Trobe) and Professor O Ragnisco (Roma Tre) The theory of (ordinary and partial) differential equations is well established and to some extent standardised. By contrast, the theory of difference equations, while more fundamental, has until recently been in its infancy, in spite of a major effort at the beginning of the 20th Century by Nörlund and the school of GD Birkhoff to establish the linear theory. Discrete systems can appear in two main guises: in the first case the independent variable is discrete, taking values on a lattice (e.g. finite-difference equations, such as recurrence relations and dynamical mappings), in the second case the independent variable is continuous (e.g. analytic difference equations and even functional equations).
Very recently, however, mainly through advances in the theory of exactly integrable discrete systems and the theory of (linear and nonlinear) special functions, the study of difference equations has undergone a true revolution. For the first time good and interesting examples of nonlinear difference equations admitting exact, albeit highly nontrivial, solutions were found and this has led to the formulation of novel approaches to the classification and treatment of such equations. Thus, an area has developed where several branches of mathematics and physics, that are usually distinct, come together: complex analysis, algebraic geometry, representation theory, Galois theory, spectral analysis and the theory of special functions, graph theory, and difference geometry.
Looking at recent developments in these various fields one observes that many of the areas that are clearly on the verge of major breakthroughs have an intimate connection with discrete integrable systems. Such fields comprise: the algebraic geometry of rational surfaces and birational maps, difference Galois theory and isomonodromic deformation theory, Diophantine problems in number theory and p-adic analysis, quantum and non-commutative discrete integrable systems, representation theory of quantum algebras and associated cluster algebras as well as special functions, difference geometry and symmetries and conservation laws of discrete systems. Bringing together experts from these fields for a substantial period of time, the programme aims at bringing about important cross-fertilisation of ideas and methodologies, and thereby substantial new advances in the theory of difference equations.
Cardiac Physiome Project 29 June to 24 July 2009 Organisers: Dr RH Clayton (Sheffield), Professor P Hunter (Auckland), Dr N Smith (Oxford) and Dr S Waters (OCIAM)
Predicting physiological behaviour from experimental data combined with environmental influences is a compelling, but unfulfilled, goal of post-genomic biology. This undeniably ambitious goal is the aim of the Physiome Project and its subset the Cardiome Project which is an international effort to build a biophysically based multi-scale mathematical model of the heart. To achieve this goal requires further development of the current generation of advanced cardiac models which span an already diverse set of mathematical representations from stochastic sub-cellular regulation models to whole-organ-based sets of coupled partial differential equations. The focus of this programme will be on the development and application of the mathematical techniques which underpin the ongoing extension of this approach, and specifically to:
• integrate data from disparate sources into a common quantitative framework;
• examine the complex cause and effect relationships which exist across many temporal and spatial orders of magnitude in physiology;
• determine the appropriate level of detail to capture observable phenomena and the closely related issue of parameter identifiability;
• examine issues of model inheritance and multi-scale coupling for combining existing models together to create extended frameworks;
• define standards for the constituent electrical, mechanical and vascular classes of cardiac models.
The aim of this programme will be to debate and provide contributions from state of the art mathematical techniques for galvanising the wider research community into focused action on the emerging issues of applying mathematics and computational science to develop multi-scale computational models of physiological systems.
Non-Abelian Fundamental Groups in Arithmetic Geometry 20 July to 18 December 2009 Organisers: Professor M Kim (Purdue), Professor J Coates (Cambridge), Professor F Pop (Pennsylvania), Dr M Saidi (Exeter) and Professor P Schneider (Münster)
In the 1980’s Grothendieck formulated his anabelian conjectures that brought to an hitherto-unexplored depth the interaction between topology and arithmetic. This suggested that the study of non-abelian fundamental groups could lead to a new understanding of deep arithmetic phenomena, including the arithmetic theory of moduli and Diophantine finiteness on hyperbolic curves. A certain amount of work in recent years linking fundamental groups to Diophantine geometry intimates deep and mysterious connections to the theory of motives and Iwasawa theory, with their links with arithmetic problems on special values of L-functions such as the conjecture of Birch and Swinnerton-Dyer. In fact, the work thus far suggests that the still-unresolved section conjecture of Grothendieck, whereby maps from Galois groups of number fields to fundamental groups of arithmetic curves are all proposed to be of geometric origin, is exactly the sort of key problem that touches the core of all these areas of number theory and more.
The goal of this programme is to investigate the ideas and problems of anabelian geometry within the global context of mainstream arithmetic geometry. By bringing together leading experts in number theory and arithmetic geometry we hope to shed more light on the inter-connections between anabelian geometry and more classical Diophantine problems, and hopefully make progress towards the solution of the section conjecture.
Dynamics of Discs and Planets 12 August to 18 December 2009 Organisers: Dr A Morbidelli (Observatory of Nice), Professor RP Nelson (Queen Mary, London), Dr GI Ogilvie (Cambridge), Professor JM Stone (Princeton) and Dr MC Wyatt (Cambridge) Ever since the discovery in 1995 of an object with half the mass of Jupiter in a four-day orbit around the star 51 Pegasi, it has been clear that the dynamics of extrasolar planetary systems can be quite different from that of our solar system. More than 200 extrasolar planets have now been found, including at least 20 systems with multiple planets, some in resonant configurations. Their diversity must originate in the properties of the protoplanetary disc of dusty gas out of which they form, the dynamics of the formation of the planetary core, and the subsequent interaction of the planet with the surrounding disc, with other planets, and with the central star.
Over the past decade, there has been significant progress on the theoretical aspects of planet formation through the mechanisms of core accretion and disc gravitational instability. Our knowledge of the physical nature of protoplanetary discs has also increased dramatically from both observations and computational modelling of their (magneto-) hydrodynamics, and the growing number of systems known to have either extrasolar planets or planetesimal belts means that the outcome of planet formation is becoming more tightly constrained. Along with discoveries in the solar system’s Kuiper belt which are revising our understanding of the formation and evolution of the outer solar system, there is now a wide array of phenomena seen in all systems which is opening up new areas of celestial mechanics.
This programme will bring together world-leading researchers in disciplines including accretion disc theory, planet formation, planet-disc interaction and solar system dynamics. With such a group we seek to provide a firm theoretical basis for our understanding of extrasolar planetary systems and their formation in protoplanetary discs. The programme encompasses three themes: (1) dynamics of astrophysical discs and the numerical and analytical methods used to study them (i.e. the study of gaseous accretion discs); (2) dynamics specific to discs in which planets are forming including that formation process (i.e. the study of how solid material interacts with gaseous discs); (3) dynamics that is relevant once planets have formed (i.e. the study of solid body interactions).
Stochastic Partial Differential Equations 4 January to 2 July 2010 Organisers: Professor Z Brzezniak (York), Dr M Hairer (Warwick), Professor M Röckner (Bielefeld), Professor P Souganidis (Texas at Austin) and Dr R Tribe (Warwick)
Stochastic Partial Differential Equations are used to model many physical systems subjected to the influence of internal, external or environmental noise. They also arise when considering deterministic models from random initial conditions, or as tractable approximations to complex deterministic systems. In many cases the presence of noise leads to new phenomena with many recent examples in the physical sciences, biology and financial modelling.
The goal of the programme is to bring together the world leaders in Stochastic Partial Differential Equations working on various aspects of the theory, numerical approximations and applications, as well as in related scientific areas.
The following will be included as themes for the 6-month programme.
The study of classical problems (well-posedness, ergodicity, etc.): Kolmogorov equations, equations with constraints, analysis of operators on infinite dimensional spaces, control theory, stochastic viscosity solutions, equations with non-Gaussian or non time-decorrelated noise.
Applications: Stochastic models in fluid flow, stochastic nonlinear Schrödinger equation, stochastic Landau- Lifshitz equations, plasmas turbulence, stochastic porous media equations, branching diffusions, stochastic growth and disintegration models, interacting species models, epidemic modelling, financial modelling.
Approximation methods: Numerical schemes (including finite element, splitting etc.), rates of convergence (theory and simulations), multiscale and asymptotic problems, particle approximations, perturbation problems.
Stochastic Processes in Communication Sciences 11 January to 2 July 2010 Organisers: Professor Venkat Anantharam (UC Berkeley), Professor François Baccelli (ENS/INRIA, Paris), Dr Denis Denisov (Heriot-Watt), Professor Serguei Foss (Heriot-Watt), Professor Peter Glynn (Stanford) and Professor Takis Konstantopoulos (Heriot-Watt)
Probability theory and communications have developed hand in hand for about a century. The research challenges in the latter field (from telephone networks to wireless communications and the Internet) have spurred the development of the mathematical theory of stochastic processes, particularly in the theory of Markov processes, point processes, stochastic networks, stochastic geometry, stochastic calculus, information theory, and ergodic theory—to name but a few. Conversely, a large number of applications in communications would not have been possible without the development of stochastics.
This programme aims at the exposition of the latest developments in mathematical sciences lying on the boundary between the disciplines of stochastics and communications. The programme, and associated workshops, will be developed around the following four basic themes and their interactions:
Stochastic networks: Stochastic modelling and analysis of networks (such as modern communication networks), and, in particular, limit theorems and asymptotic analysis—macroscopic approximations, control, optimisation and other mathematical techniques.
Spatial networks: Methods based on stochastic geometry, random graphs, percolation, and random matrix theory; space-time modelling with applications in wireless networks.
Statistics of networks: Advanced simulation theory and techniques (scalability, rare-events, long-range dependence, heavy tails), inverse problems, probing and measurements.
Information theory and networks: Information transmission problems in modern networks taking into account the presence of feedback, burstiness of traffic, spatial aspects and mobility; filtering and signal processing.
Statistical Challenges Arising from Genome Resequencing 12 July to 6 August 2010 Organisers: Professor D Balding (Imperial College London), Professor C Holmes (Oxford) and Professor G McVean (Oxford) The current generation of high-throughput genetic and genomic platforms has had a great impact on biomedical research, and given new impetus to studies of molecular mechanisms of genetic disease and to systems biology. The next big technological step forward is the advent of cheap, fast sequencing platforms that will allow near-complete genome sequences to be quickly and affordably obtained from individual members of any species. Individual genomes from humans, their pathogens, and model organisms will have an enormous impact on population genetics and evolutionary theory, as well as on epidemiology, particularly our understanding of infectious disease.
The motivation for our workshop is to bring together leading mathematical and biological researchers in an interdisciplinary environment to discuss the mathematical, statistical and computational challenges that lie ahead. We plan to discuss the most pressing open problems and the most promising avenues of future research necessary to deliver the full benefits of genome resequencing.
Precise topics are yet to be decided in this fast-moving field, but they are likely to involve sequence assembly, and applications of resequencing to genetic epidemiology and metagenomics. The mathematical techniques involved will be wide-ranging, including statistical and machine-learning techniques for high-dimensional classification and regression, as well as techniques from signal processing and various mathematical models of evolutionary processes.
Partial Differential Equations in Kinetic Theories 16 August - 22 December 2010 Organisers: Professor JA Carillo (ICREA, Barcelona), Professor S Jin (Wisconsin), and Professor PA Markowich (Cambridge) Kinetic equations occur naturally in the modelling of the collective motion of large individual particle ensembles such as, for example, molecules in rarefied gases, beads in granular materials, charged particles in semiconductors and plasmas, dust in the atmosphere, cells in biology, or the behaviour of individuals in economical trading. Generally, huge interacting particle systems cannot efficiently be described by the individual dynamics of all particles due to overwhelming complexity but clearly some input from the microscopic behaviour is needed in order to bridge from microscopic dynamics to the macroscopic world, typically rendered in terms of averaged quantities. This leads to classical equations of mathematical physics: the Boltzmann equation of rarefied gas dynamics, the fermionic and bosonic Boltzmann equations and the relativistic Vlasov-Maxwell system, to name just a few. Kinetic theory has produced as a spin-off many new mathematical tools in the last 20 years: renormalized solutions of transport equations by R DiPerna and P-L Lions, averaging lemmas by the French kinetic school, entropy dissipation tools (which have been extended methodologically and used far beyond kinetic theory) are just some of the highlights of new analytical PDE methods stemming from kinetic theory. Another recent landmark in this field has been the proof of the hydrodynamic limit process of the renormalized solutions of the Boltzmann equation towards (weak) Leray solutions of the Navier-Stokes equations by F Golse and L Saint-Raymond. On the other hand, kinetic theory has different scientific viewpoints ranging from applied mathematical and physical modelling to stochastic analysis, numerical analysis of PDEs and in many important cases extensive numerical simulations. The main objective of this programme is aimed at advancing Partial Differential Equations (PDEs) research in kinetic theories and its impact in the applied sciences highlighting selected modern application areas. This effort has to be understood from a global perspective of research in PDEs bringing together mathematical modelling, analysis, numerical schemes and simulations in a feedback loop of synergies. The three selected newly emerging application areas of kinetic theories are kinetic modelling in biology, coupled fluid-particle models and PDE Models for quantum fluids.
Moduli Spaces 4 January - 1 July 2011 Organisers: Professor PE Newstead (Liverpool), Professor L Brambila-Paz (CIMAT, Mexico), Professor O García-Prada (CSIC, Mexico) and Professor R Thomas (Imperial College London)
Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the mid-nineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notable with the infusion of ideas from physics after 1980. The programme will focus on the following topics: (i) Moduli of bundles and augmented bundles on algebraic curves: more specifically Higgs bundles, parabolic bundles, coherent systems, principal bundles. (ii) Relationship of moduli spaces to topology, Teichmüller theory and hyperbolic geometry – this relationship takes place in the study of representations of a surface group in a real Lie group and involves Higgs bundle theory, bounded cohomology, Anosov systems, cluster varieties, tropical algebraic geometry; there is a very rich geometric structure and the various points of view are complementary, the relationship between them yet to be understood. (iii) Moduli of algebraic varieties – recent work has made exciting connections with the subject of special metrics in Kähler geometry. This has led to the revisiting of the old unsolved question of giving an intrinsic criterion for the stability of algebraic varieties. (iv) Moduli in derived categories – the study of moduli spaces in derived categories is a new and highly promising area of research, involving in particular new notions of stability. We should emphasise that the topics are not independent. There are obvious links between (i) and (ii), while (iv) has already had an impact on all the other topics and we believe that this impact is likely to get stronger. The central aims of the programme are to bring together experts in various aspects of moduli theory and related areas, to advance these topics, and to introduce research students and post-docs to the wealth of ideas and problems in them. As stated above, the interdependence of the topics we have identified is crucial to the development of the theory, and a major goal is to develop these ideas further.
Inverse Problems 25 July - 21 December 2011 Organisers: Professor M Brown (Cardiff), Professor T Fokas (Cambridge), Professor S Kurylev (University College London), Professor WRB Lionheart (Manchester) and Professor WW Symes (Rice)
Many important real world problems give rise to an Inverse Problem (IP). These include medical imaging, non-destructive testing, oil and gas exploration, land-mine detection and process control. For example, in the exploration for oil and gas, one needs to assess the structure of the interior of the earth from observations made at the surface. Typically, an explosion is created and the resulting shockwaves together with their reflections are used to build a model of the structure of the earth. In magnetoencephalography one needs to determine the electric current in the neurones from the measurement of the magnetic field outside the head. In the field of medical imaging IP forms an important tool in diagnostic investigations. For example, PET and SPECT are two modern imaging techniques whose success is dependent on solving IP.
The mathematical machinery needed for solving various IPs is mainly founded in mathematical analysis and uses tools from functional analysis, function theory, conformal maps, spectral theory, the theory of PDE’s, integral equations, and micro-local and global analysis. In recent years tools from differential geometry, stochastic analysis etc. are becoming important. Moreover, in order to realise the solution to many applied problems in a useful way, the tools of numerical analysis and scientific computing are needed.
We intend this programme to help cross-fertilise ideas between scientists by providing them with the opportunity to work on important problems with experts from other groups. We intend to focus on the following topics during the period of the programme: Inverse spectral problems, Analytic and geometric methods for IP, Stochastic methods, Numerical methods, and Application of IP to industry, medicine, finance, biology, and exploration seismology; and plan to organise several workshops which focus on these highlighted areas, as well as a tutorial meeting.
Past Programmes
Design of Experiments 21/07/08–15/08/08
Statistical Theory and Methods for Complex, High-Dimensional Data 07/01/08–27/06/08
Combinatorics and Statistical Mechanics 14/01/07–04/07/08
Phylogenetics 03/09/07–21/12/07
Strong Fields, Integrability and Strings 23/07/07–21/12/07
Bayesian Nonparametric Regression: Theory, Methods and Applications 30/07/07–24/08/07
Highly Oscillatory Problems: Computation, Theory and Application 15/01/07–06/07/07
Analysis on Graphs and its Applications 08/01/07–29/06/07
Stochastic Computation in the Biological Sciences 23/10/06–15/12/06
The Painlevé Equations and Monodromy Problems 04/09/06–29/09/06
Noncommutative Geometry 24/07/06–22/12/06
Spectral Theory and Partial Differential Equations 17/07/06–11/08/06
Logic and Algorithms 16/01/06–07/07/06
Principles of the Dynamics of Non-Equilibrium Systems 09/01/06–30/06/06
Global Problems in Mathematical Relativity 08/08/05–23/12/05
Pattern Formation in Large Domains 01/08/05–23/12/05
Developments in Quantitative Finance 24/01/05–27/07/05
Model Theory and Applications to Algebra and Analysis 17/01/05–15/07/05
Magnetohydrodynamics of Stellar Interiors 06/09/04–17/12/04
Quantum Information Science 16/08/04–17/12/04
Magnetic Reconnection Theory 02/08/04–27/08/04 Random Matrix Approaches in Number Theory 26/01/04–16/07/04
Statistical Mechanics of Molecular and Cellular Biological Systems 19/01/04–09/07/04
Granular and Particle-Laden Flows 01/09/03–19/12/03
Interaction and Growth in Complex Stochastic Systems 21/07/03–19/12/03
Spaces of Kleinian Groups and Hyperbolic 3-Manifolds 21/07/03–15/08/03
Nonlinear Hyperbolic Waves in Phase Dynamics and Astrophysics 27/01/03–11/07/03
Computational Challenges in Partial Differential Equations 20/01/03–04/07/03
Computation, Combinatorics and Probability 29/07/02–20/12/02
New Contexts for Stable Homotopy Theory 02/09/02–20/12/02
Foams and Minimal Surfaces 29/07/02–23/08/02
M-Theory 04/02/02–19/07/02
Higher Dimensional Complex Geometry 04/02/02–19/07/02
From Individual to Collective Behaviour in Biological Systems 10/09/01–19/12/01
Integrable Systems 23/07/01–19/12/01
Surface Water Waves 13/08/01–31/08/01
Managing Uncertainty - New Analysis Tools for Insurance, Economics and Finance 23/07/01–10/08/01
Nonlinear Partial Differential Equations 08/01/01–06/07/01
Symmetric Functions and Macdonald Polynomials 08/01/01–06/07/01
Geometry and Topology of Fluid Flows 04/09/00–17/12/00
Singularity Theory 24/07/00–22/12/00
Quantized Vortex Dynamics and Superfluid Turbulence 07/08/00–25/08/00
Free Boundary Problems in Industry 17/07/00–04/08/00
Strongly Correlated Electron Systems 05/01/00– 07/07/00
Ergodic Theory, Geometric Rigidity and Number Theory 05/01/00–07/07/00
Mathematical Developments in Solid Mechanics and Materials Science 06/09/00–17/12/00
Structure Formation in the Universe 19/07/99– 17/12/99
Complexity, Computation and the Physics of Information 10/05/99–20/08/99
Turbulence 04/01/99–02/07/99
Mathematics and Applications of Fractals 06/01/99–23/04/99
Biomolecular Function and Evolution in the Context of the Genome Project 21/07/98–19/12/98
Nonlinear and Nonstationary Signal Processing 21/07/98–19/12/98
Arithmetic Geometry 05/01/98–03/07/98
Dynamics of Astrophysical Discs 05/01/98–03/07/98
Neural Networks and Machine Learning 21/07/97–19/12/97
Disordered Sytems and Quantum Chaos 21/07/97–19/12/97
Non-Perturbative Aspects of Quantum Field Theory 05/01/97–07/07/97
Representation Theory of Algebraic Groups and Related Finite Groups 05/01/97–07/07/97
Four-Dimensional Geometry and Quantum Field Theory 04/11/96–13/12/96
Mathematical Modelling of Plankton Population Dynamics 29/07/96–04/09/96
Mathematics of Atmosphere and Ocean Dynamics 08/07/96–19/12/96 Computer Security, Cryptology and Coding Theory 01/01/96–30/06/96
Dynamics of Complex Fluids 01/01/96–30/06/96
From Finite to Infinite Dimensional Dynamical Systems 01/07/95–31/12/95
Semantics of Computation 01/07/95–31/12/95
Financial Mathematics 01/01/95–30/06/95
Exponential Asymptotics 01/01/95–30/06/95
Symplectic Geometry 01/07/94–31/12/94
Topological Defects 01/07/94–31/12/94
Cellular Automata Aggregation and Growth 01/01/94–30/06/94
Geometry and Gravity 01/01/94–30/06/94
Random Spacial Process 01/07/93–31/12/93
Computer Vision 01/07/93–31/12/93
Epidemic Models 01/01/93–30/06/93
L-functions and Arithmetic 01/01/93–30/06/93
Dynamo Theory 01/07/92–31/12/92
Low Dimensional Topology and Quantum Field Theory 01/07/92–31/12/92
For further information, contact the Director, Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK; tel. 01223 335999; e-mail [email protected]. Information can also be found at www.newton.ac.uk