Banff International Research Station for Mathematical Innovation and Discovery BIRS 2007/2008 Scientific Report Preface The Banff International Research Station (BIRS) is now a collaborative Canada-US-Mexico venture that will continue to provide for the world’s scientific community an environment for creative interaction and the exchange of ideas, knowledge and methods within the Mathematical Sciences and with related sciences and industry. In 2007, BIRS reached its full potential, hosting over 2,000 scientists from more than 40 countries by running 48 weeks of programming (up from 44 weeks in 2006 and 40 weeks in 2005). In spite of this substantial expansion of opportunities at BIRS, the extraordinary response of the world’s scientific community continues unabated to contribute extremely high quality submissions, with over 300 proposed activities competing for the 96 available weeks in 2007 and 2008. During 2007 and 2008, BIRS was once again home to a dazzling array of scientific activities. Besides the tremendously successful 5-day Workshops and Research-in-Teams programs, BIRS hosted Fo- cused Research Groups, Collaborative Research Teams, leadership retreats, gatherings for women in mathematics, First Nations math education, mentoring for engineering academia, summer schools in emerging areas, students’ modeling camps, workshops on industrial mathematics, and training sessions for Math Olympiads teams. The BIRS program touched on every aspect of the mathematical sciences, but also offered op- portunities for highly innovative themes such as Mathematics Education via the Arts, Mathematical Methods in Philosophy, First Nations Math Education, and Modeling the Impact of Policy Options during Public Health Crises. Front and centre were topics dealing with some of the most pressing issues of modern society: Data Mining and Machine Learning; Complex Data Structures in the Health, Social and Environmental Sciences; Statistical Methods for High-throughput Genetic Data, Stochastic Dynamical Systems and Climate Modeling; Mathematics and the Environment: Energy Risk, Environmental Uncertainty and Public Decision Making. At BIRS, traditional barriers between the various sciences are all but forgotten. Workshops such as the one on The Mathematics of Knotting and Linking in Polymer Physics and Molecular Biology essentially involves all the basic sciences, while engineering and the applied sciences are well rep- resented by topics such as Mathematical Methods for Medical Image Analysis, and Physics-Based Mathematical Models of Low-Dimensional Semiconductor Nano-structures. Last but not least, I should mention the extremely successful summer school on The Stable Trace Formula, Automorphic Forms, and Galois Representations, led by James Arthur (University of To- ronto), Michael Harris (Université de Paris VII), and Eric Urban (Columbia University). This was a high-calibre gathering that built on the so-called “Paris Project” which is expected to produce four books, the last of which is still almost completely open in anticipation of contributions from the new generation of number theorists present at the 2008 BIRS school. Many thanks to the over two hundred organizers and the more than 4,000 participants who have made the last two years of BIRS such an unqualified success. Nassif Ghoussoub, FRSC Scientific Director, Banff International Research Station Distinguished University Scholar, University of British Columbia Adjunct Professor, University of Alberta 2 Contents 2007 5-day Workshops ............................................................................................. 7 2-day Workshops ............................................................................................ 59 Summer Schools, Research in Teams, Focused Research Groups ................ 73 2008 5-day Workshops ............................................................................................. 3 2-day Workshops ............................................................................................ 57 Summer Schools, Research in Teams, Focused Research Groups ................ 65 3 4 5-Day Workshops 2007 Jan 14 Jan 19 Mathematical Programming in Data Mining and Machine Learning Jan 21 Jan 26 Innovations in Mathematics Education via the Arts Jan 28 Feb 02 Nonholonomic Dynamics and Integrability Jan 28 Feb 02 Numerical Analysis of Multiscale Computations Feb 4 Feb 09 Explicit Methods for Rational Points on Curves Feb 11 Feb 16 Operator Structures in Quantum Information Theory Feb 18 Feb 23 Mathematical Methods in Philosophy Feb 25 Mar 02 Topology Mar 04 Mar 09 North American Workshop on Tropical Geometry Mar 11 Mar 16 Mathematical Developments around Hilbert’s 16th Problem Mar 18 Mar 23 Contemporary Schubert Calculus and Schubert Geometry Mar 25 Mar 30 Interactions of Geometry and Topology in Low Dimensions Apr 01 Apr 06 Discrete Geometry and Topology in Low Dimensions Apr 08 Apr 13 Complex Data Structures in the Health, Social and Environmental Sciences Apr 15 Apr 20 Stochastic Dynamical Systems and Climate Modeling Apr 22 Apr 27 The Many Strands of the Braid Groups May 8 May 13 Mathematics and the Environment: Energy Risk, Environmental Uncertainty and Public Decision Making May 13 May 18 New Applications and Generalizations of Floer Theory May 20 May 25 The Mathematics of Knotting and Linking in Polymer Physics and Molecular Biology May 27 Jun 01 Algebraic Lie Theory Jun 03 Jun 08 Modular Forms: Arithmetic and Computation Jun 10 Jun 15 Commutative Algebra and Its Interaction with Algebraic Geometry Jun 17 Jun 22 Geometric Inequalities Jun 24 Jun 29 Statistical Methods for High-throughput Genetic Data Jul 01 Jul 06 Bioinformatics, Genetics and Stochastic Computation: Bridging the Gap Jul 08 Jul 13 L-functions, Ranks of Elliptic Curves, and Random Matrix Theory Jul 15 Jul 20 Quadrature Domains and Laplacian Growth in Modern Physics Jul 22 Jul 27 Mentoring for Engineering Academia II Jul 29 Aug 03 Topological and Geometric Rigidity Aug 05 Aug 10 Canada-China Workshop on Industrial Mathematics Aug 12 Aug 17 Geometric Mechanics: Continuous and Discrete, Finite and Infinite Dimensional Aug 19 Aug 24 Operator Spaces and Group Algebras Aug 26 Aug 31 Loss of Compactness in Nonlinear PDE: Recent Trends Sep 02 Sep 07 Hochschild Cohomology of Algebras: Structure and Applications Sep 09 Sep 14 Applications of Macdonald Polynomials Sep 16 Sep 21 Group Embeddings: Geometry and Representations Sep 23 Sep 28 Trends in Applied Harmonic Analysis Sep 30 Oct 05 Entropy of Hidden Markov Processes and Connections to Dynamical Systems Oct 07 Oct 12 Recent Progress on Nonlinear Elliptic and Parabolic Problems and Related Abstract Methods Oct 14 Oct 19 Infinite Graphs Oct 21 Oct 26 Low-dimensional Topology and Number Theory Oct 28 Nov 02 International Workshop on Robust Statistics and R Nov 04 Nov 09 Mathematical Methods for Medical Image Analysis Nov 11 Nov 16 Modern Approaches in Asymptotics of Polynomials Nov 18 Nov 23 Physics-Based Mathematical Models of Low-Dimensional Semiconductor Nanostructures: Analysis and Computation Nov 25 Nov 30 Discontinuous Galerkin Methods for Partial Differential Equations Dec 02 Dec 04 First Nations Math Education I Dec 04 Dec 07 First Nations Math Education II Dec 09 Dec 14 Minimal Submanifolds and Related Problems 5 2-Day Workshops 2007 Mar 30 Apr 01 Third Northwest Functional Analysis Symposium Apr 13 Apr 15 Symbolic Computer Algebra in Theoretical Physics Apr 20 Apr 22 Math Fair Workshop May 25 May 27 Discrete-time Graph Processes and Games Jun 15 Jun 17 Stochasticity in Biochemical Reaction Networks Jun 22 Jun 24 Dynamical Systems and Applications Jun 29 Jul 01 Statistical Science for `omic Research in Canada Jul 27 Jul 29 Diversity in the Mathematics and Scientific Community I and II Aug 10 Aug 12 PHAC-MITACS Joint Symposium on Modeling Sexually Transmitted and Blood-borneInfections Aug 31 Sep 02 Intuitive Geometry Sep 07 Sep 09 Mathematical Modelling of Water Resource Allocation Strategies Sep 14 Sep 16 Affine Schubert Calculus Workshop: Design and Implementation of Research Tools in MuPAD-Combinat Summer Schools Apr 29 May 08 Mathematics and the Environment: Energy Risk, Environmental Uncertainty and Public Decision Making Jul 10 Jul 22 2007 Summer IMO Training Camp Research In Teams Mar 18 Mar 25 Graph Colouring Problems Arising in Telecommunications May 15 May 20 Bioeconomics of Invasive Species: Integrating Ecology, Economics and Management Jun 03 Jun 10 String Theory and Inflationary Cosmology Jun 29 Jul 08 Mapping Quantitative Traits in Humans Aug 05 Aug 12 Recent Advances in Mathematical Relativity Aug 12 Aug 19 Noncommutative Duality in Dynamical Systems Aug 20 Aug 28 Sieve Methods Aug 26 Sep 09 Conformal and CR geometry: Spectral and Nonlocal Aspects Focused Research Groups Mar 04 Mar 11 Quasiconformal Homogeneity: Energy Methods and Sharp Bounds Mar 25 Apr 01 The Xi-transform May 06 May 13 Stochastic Models of Influenza Dynamics May 20 May 30 Global Attraction to Solitary Waves in Nonlinear Dispersive Hamiltonian Systems Jun 17 Jun 24 Mathematics and Pedagogy Project Jul 22 Jul 29 Integrability, Gauge Fields and Strings 6 Banff International Research Station 2007 5-Day Workshops 7 8 Mathematical Programming in Data Mining and Machine Learning January 14 - 19, 2007 Organizers: Michael Jordan (UC-Berkeley) Katya Scheinberg (IBM TJ Watson Research Center) Jiming Peng (University of Illinois at Urbana-Champaign) Dale Schuurmans (University of Alberta) Tomaso Poggio (MIT) Tamás Terlaky (McMaster University This workshop