## PIMS Postdoctoral Colloquium 4

- Date: 03/26/2009

Mark MacDonald, Department of Mathematics, UBC

University of British Columbia

Chow Motives of Quadrics

Abstract: A Chow motive of an algebraic variety may be thought of as an attempt to define a universal cohomology theory for algebraic varieties, through the use of the Chow ring. The Chow ring in algebraic geometry is an analog of the cohomology ring of a topological space.

In this talk I will define and describe Chow motives of algebraic varieties, with a focus on quadrics - which are the zero sets of degree 2 homogeneous polynomials. The reason for the focus on quadrics is because their Chow motives may be nicely decomposed and this decomposition can be easily visualized with a helpful diagram. Also, I may have time to mention some new results, where I have explicitly decomposed the Chow motives of a particular class of quadrics.

Postdoctoral Colloquium