|TITLE:||Cocycles and cocycle categories|
|SPEAKER:||Rick Jardine (University of Western Ontario)|
|DATE:||Vendredi, 21 Octobre 2005|
|ROOM:||Fauteux Hall, Room 351|
Cocycles and the cohomology elements that they represent are fundamental objects of study in algebra, geometry and topology. This talk will survey standard examples, and then present a new unified point of view for these constructions within the framework of cocycle categories. Cocycle categories are ubiquitous in homotopy theory, and their sets of path components represent morphisms in a large family of homotopy categories. The cocycle category approach is a flexible tool for demonstrating homotopy classifications results for equivalence classes of objects with structure; some applications will be displayed.
About the speaker: Rick Jardine is a Canada Research Chair in Applied Homotopy Theory in the Department of Mathematics., University of Western Ontario. Rick Jardine received his Phd from U.B.C. in 1981 in algebraic homotopy theory and K-theory. Since 1990 he has been a Professor in the Mathematics Department at the University of Western Ontario. In 1998-2003 he was Chairman of the Department, and since 2002 a Canada Research Chair. Among his honours, he was a Dickson Instructor at the University of Chicago (1982-84), an NSERC University Research Fellow and later Distinguished University Professor at the University of Western Ontario, an Alfred P. Sloan Fellow (1987-89), CMS Coxeter-James Lecturer (1992), and gave the Poincare Lectures at the Fields Institute (1996). He has published two books (Simplicial Homotopy Theory, with P. Goerss, in 1999) and and Generalized Etale Cohomology Theories (1997), and edited two more.
Rick Jardine's research is primarily in algebraic K-theory and homotopy theory, focussing recently on cohomology of algebraic groups and Motivic homotopy 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 culminated 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.