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Lecture 1: Cutting and pasting in algebraic geometry, and the motivic zeta function

Date: 
Thu, 17/03/201614:30
Location: 
Lecture Hall 2
Lecturer: 
Prof. Ravi Vakil, Stanford University
Given some class of "geometric spaces", we can make a ring as follows.
  1. (additive structure) When U is an open subset of such a space X,
    [X] = [U] + [(X \ U)];
  2. (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 give an introduction to the Grothendieck ring of varieties, giving a survey of a small portion of interesting results in the field due to various people (Kapranov, Cheah, Larsen-Lunts, Liu-Sebag, Bittner, Borisov, Litt, ...). Time permitting, I will discuss joint work with Melanie Matchett Wood.