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Zassenhaus Lecture - Ravi Vakil

Ravi Vakil
March 20, 2017
4:10 pm - 5:10 pm
Smith Lab 1009

Title: Cutting and pasting in (algebraic) geometry

Speaker: Ravi Vakil (Stanford University)

Abstract: Given some class of "geometric space", we can make a ring as follows.

  1. (additive structure) When $U$ is an open subset of such a space $X$, $[X] = [U] + [(X \setminus U)]$;
  2. (multiplicative structure) $[X \times Y] = [X] [Y]$.

In the algebraic setting, this ring (the "Grothendieck ring of varieties") contains surprising "stabilization" 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.

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