Cutting and pasting in algebraic geometry

School of Mathematics Colloquium
Wednesday, June 11, 2014 - 3:30pm
1 hour (actually 50 minutes)
Skiles 006
Stanford University
Given some class of "geometric spaces", we can make a ring as follows. (i) (additive structure) When U is an open subset of such a space X, [X] = [U] + [(X \ U)] (ii) (multiplicative structure) [X x Y] = [X] [Y].In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising structure, connecting geometry to arithmetic and topology.  I will discuss some remarkable statements about this ring (both known and conjectural), and present new statements (again, both known and conjectural).  A motivating example will be polynomials in one variable. (This talk is intended for a broad audience.)  This is joint work with Melanie Matchett Wood.