Collaborative Research Groups
A Collaborative Research Group (CRG) typically consists of researchers with overlapping research interests and with a common desire to collaboratively develop some aspects of their research programs. A CRG will organize joint seminars and workshops, make joint PDF appointments, and perhaps develop joint graduate training programs, but will have the potential to do much more, given the resources and organizational structure of PIMS.
Current and Upcoming Collaborative Research Groups
2025—2028
Diagram Categories in Homotopy Theory
This CRG will study diagram categories in homotopy theory, focusing on functor calculus, equivariant homotopy theory, and polyhedral products. These are active and important fields of research with connections to each other and to other areas of...
2024—2027
Structure-Preserving Discretizations and their Applications
There is a dedicated CRG Website for this CRG, please see that site for up to date information. Nature abounds with mathematical structure. Computational models of nature, however, often do not reflect such structure, and hence their predictions may...
2023—2026
Forecasting and Mathematical Modeling for Renewable Energy
Wind and solar energy are expected to be the primary sources of electricity in the future world. Both wind and solar power are stochastic and intermittent as they are weather driven. The main purpose of this CRG is to develop meso, submeso and micro...
2022—2025
L-Functions in Analytic Number Theory
Analytic number theory focuses on arithmetic questions through the lens of L-functions. These generating series encode arithmetic information and have connections with a host of other mathematical fields, such as algebraic number theory, harmonic...
Past Collaborative Research Groups
2021—2024
Movement and Symmetry in Graphs
The Movement and Symmetry in Graphs Collaborative Research Group will look at Graph Theory. Graph theory is a thriving discipline that lies at the interface of computer science and pure mathematics; the goal of this CRG is to make the prairie region...
2021—2024
Pacific Interdisciplinary hub on Optimal Transport
The Pacific Interdisciplinary hub on Optimal Transport (PIHOT) is a Collaborative Research Group examining the research and applications of Optimal Transportation across a wide audience of researchers, students, industry, policy makers and the...
2020—2023
Novel Techniques in Low Dimension: Floer Homology, representation theory and algebraic topology
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...
2020—2023
Quantum Topology and its Applications
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...
2018—2021
High Dimensional Data Analysis
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...
2016—2019
Geometric Analysis
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...
2016—2019
Geometric and Cohomological Methods in Algebra
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...
2015—2018
Applied Partial Differential Equations: Modeling, Analysis, and Computation
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...
2015—2018
Explicit Methods for Abelian Varieties
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...
2014—2018
Applied, Algebraic and Geometric Topology
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...
2014—2017
Applied Combinatorics
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...
2013—2016
Geometry and Physics
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...
2012—2015
Algorithmic Theory of Networks
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...
2012—2015
Optimization: Theory, Algorithms and Applications
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...
2012—2014
Applied and Computational Harmonic Analysis
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...
2010—2014
Mathematics of Quantum Information
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...
2010—2013
L-functions and Number Theory
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...
2009—2012
Operator Algebras and Non-commutative Geometry
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...
2008—2011
Partial Differential Equations
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...
2008—2010
Bayesian Modeling and Computation for Networks
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...
2007—2010
Climate Modelling
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...
2007—2010
Differential Geometry and Analysis
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...
2007—2010
Envirometrics
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...
2007—2009
Geophysical and Complex Fluid Dynamics
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...
2006—2008
Geometric and Harmonic Analysis
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...
2006—2008
Mathematical Finance
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...
2006—2008
Mathematical Modeling
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...
2005—2007
Algebraic Geometry, Group Cohomology, Representation Theory (AG-GC-RT)
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...
2005—2007
Inverse Problems
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...
2005—2007
Quantum Topology
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...