Past CRGs

Recent advances have completely reshaped the landscape of geometric topology. On the one hand, Perelman's revolutionary work on Ricci flow confirms Thurston's geometrization conjecture, establishing that topological 3-manifolds can be decomposed into...

Of all of the scientific discoveries of the past few decades, one of the most promising — and surprising — is that of topological materials. These materials have the potential to change not only what is done in labs but also what we do in our homes...

There are fundamental open questions that limit the industrial uptake of ideas from the mathematics of high-dimensional data and their application in practice. These include bridging the gap between the sampling required by theory and what is...

This three-year long CRG aims to enhance connections and stimulate collaborations among the mathematicians at the four institutions (the Australian National University, the Beijing International Center for Mathematical Research, the University of...

Overview Universities in Western Canada have been traditionally strong in algebra, in particular in representation theory and the theory of Lie algebras. More recently, the algebra community in Western Canada was solidified and strengthened by the...

Overview The scientific focus of this CRG will be to study nonlinear partial differential equations (PDEs) with particular emphasis on problems involving pattern formation, defined in the broadest sense. Specific topics in this area include the study...

Overview Abelian varieties are fundamental objects in algebraic geometry with a long, rich history of study. They are indispensable in number theory, and an important source of practical settings for cryptography. Although there are wide-ranging...

Topology is a central area of mathematics, with broad interactions with many other fields as well as emerging applications to subjects such as robotics, economics, computer science and large data set analysis. The subject often is divided into its...

The CRG in Applied Combinatorics will address problems at the interface of discrete mathematics and the physical sciences. The key objects are beautiful and subtle combinatorial models, which are of interest to both pure and applied mathematicians...

Pure mathematics and fundamental physics, historic partners for centuries, grew apart during the first half of the 20th century. This changed with the emergence of gauge theory in particle physics and, still more strikingly, the string-theoretic...

OVERVIEW The technology revolution of the 1990s and the 2000s owes much of its existence to the advances in computer networking technologies. These advances have made profound changes in how we model, construct/modify, maintain, use, and, ultimately...

The linear programming problem: Is there a polynomial time algorithm over the real numbers which decides the feasibility of the linear system of inequalities Ax ≥ b? (Problem 9 of 18 in Mathematical Problems for the Next Century by S. Smale) Our...

Overview Applied and Computational Harmonic Analysis is an interdisciplinary branch of modern mathematics and is concerned with the applied and computational aspects of harmonic analysis and approximation theory, with special emphasis on wavelet...

Overview Quantum information science is an interdisciplinary research endeavour that brings together computer scientists, mathematicians, physicists, chemists, and engineers to develop revolutionary information processing and communication...

Overview Number theory is a subject as diverse as it is ancient, and this diversity is well represented in the mathematics departments of PIMS universities. These universities are home to academics with expertise in algebraic and analytic number...

Overview The subject of operator algebras has its origins in the work of Murray and von Neumann concerning mathematical models for quantum mechanical systems. During the last thirty years, the scope of the subject has broadened in a spectacular way...

Overview Partial Differential Equations is a large subject with a history that dates back to Newton and Leibniz. They form the basis for many mathematical models in the sciences and in economics, yielding such famous equations as the Euler and Navier...

Overview This PIMS funded collaborative research group focuses on Bayesian methods for network analysis, paying special attention to model design and computational issues of learning and inference. Bayesian inference is an approach to statistics in...

Overview This will be a multidisciplinary effort bringing together mathematicians and earth/ocean scientists to understand some of the many outstanding problems in climate modelling and numerical weather prediction. Particular emphasis will be placed...

Overview The general theme of the Differential Geometry and Analysis CRG is the use of analytical methods to solve geometric problems, such as constructing special submanifolds of given manifolds: minimal hypersurfaces, which are important in the...

Overview The eventual goal of this project is to develop a multi-site, distributed environmetrics research centre. The main research themes are: statistical and deterministic models in georisk analysis; modelling space-time fields; agroclimate risk...

Overview The primary focus is the mathematical modeling of complex and classic geophysical fluid dynamics, which are key elements in many geophysical phenomena such as volcanic eruptions, mud slides and avalanches. Bringing sophisticated mathematical...

Overview Geometric functional analysis is concerned with geometric and linear properties and structure of finite- and infinite-dimensional Banach spaces and their unit balls. An asymptotic point of view is based upon expressing such properties in...

Overview There is a significant research activity in Mathematical Economics in Western Canada. However, this research has no supporting network. Our goal is to promote interdisciplinary cooperations among Canadian experts in mathematics, finance...

Overview The primary focus of the proposed CRG is mathematical modeling driven by biological applications. The goal is to promote research and cooperation both within specific research areas and across different areas of application. In keeping with...

Overview Algebraic geometry is a mathematical discipline which uses the techniques and tools of algebra (e.g. rings, ideals and fields) to attack geometric problems. The fundamental objects which algebraic geometers study are algebraic varieties, the...

Overview Inverse Problems (IP) are problems where causes for a desired or observed effect are to be determined. An important example is to determine the density distribution inside a body from measuring the attenuation of X-rays sent through this...

Overview The problems of interest in this CRG are (i) the so-called "many-body problem" in non-relativistic physics, particularly on lattices in low spatial dimension; and (ii) the problem of finding a universal quantum computer which evades...

Overview Much of the original motivation for th study of spatially interactive stochastic systems came from stochastic models in statistical physics. An intensive area of recent research centres around the idea that complex local dynamics can lead to...

Overview The PIMS community has an active group of researchers in topology and related fields. Their research may be roughly divided into two major themes: geometric and algebraic. Among the geometric issues being studied by PIMS topologists are the...