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...