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Rick Jardine
Ph.D., University of British Columbia (1981)
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Telephone: 519-661-3638 x 86516
Fax: 519-661-3610
E-mail: jardine@uwo.ca
Jardine's research is in homotopy theory and its applications.
Algebraic topology is the study of algebraic approximations of space, and has been one of the driving forces of Mathematics since early in the twentieth century; it effectively began with the work of Poincaré in the late 1890s. The theory acquired great depth and computational power over the years, and achieved a precise level of axiomatic simplicity with Quillen's introduction of closed model structures in the 1960s. At the same time, the Grothendieck school in Paris began a grand project to apply the wealth of homotopy theoretic calculational methods to algebraic geometry and number theory. This enterprise continues to this day, and has always been a central theme of research in algebraic K-theory.
The modern period for this branch of homotopy theory began in the mid 1980s with the discovery of closed model structures for wide classes of simplicial objects in algebraic geometry by Jardine and Joyal, and has progressed in recent years with the introduction of motivic homotopy theory by Morel and Voevodsky in connection with Voevodsky's celebrated proof of the Milnor Conjecture. These homotopy theories that arise in algebraic geometry are widely applicable: every sheaf cohomology invariant, for example, is represented by a presheaf of spectra in an appropriate stable homotopy category. It is also clear now, as a result of ongoing research of Jardine and others, that the homotopy theory of simplicial presheaves is the right context for non-abelian cohomology theories, and for the theory of stacks and higher stacks.
Jardine is the coauthor, with Paul Goerss (Northwestern University), of the book Simplicial Homotopy Theory, which was published by Birkhäuser in 1999. The book was the first to appear in the subject in over 25 years; it describes much of the present state of the art in the combinatorial approach to homotopy theory.
Combinatorial homotopy theory is used throughout modern Mathematics, and is finding new applications in Science and Engineering, particularly in the study of networks, the development of models for parallel processing, and geometric analysis of large data sets. Jardine is the cofounder, with Gunnar Carlsson of Stanford University, of the "Algebraic Topological Methods in Computer Science" conference series (held at Stanford in 2001, Western Ontario in 2004, and Paris VII in 2008), and was a co-organizer for the research program "Computational Applications of Algebraic Topology" which was held at the Mathematical Science Research Institute in Berkeley through the Fall of 2006. Jardine was the Lead Organizer for the research program "Geometric Applications of Homotopy Theory" which ran at the Fields Institute during the first six months of 2007.
Jardine is the cofounder, with Dan Grayson (University of Illinois at Urbana-Champaign), of the Algebraic K-theory Preprint Archive at the University of Illinois at Urbana-Champaign. This was one of the original subject-area preprint servers in Mathematics, and is still among the most successful. Grayson and Jardine are joint cofounders of the Great Lakes K-theory series of conferences, which began in 1995 and has since been held on an annual basis.
