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University of Cambridge > Talks.cam > Algebraic Geometry Seminar > COW: Cutting and pasting in algebraic geometry

## COW: Cutting and pasting in algebraic geometryAdd to your list(s) Download to your calendar using vCal - Ravi Vakil (Stanford)
- Thursday 21 April 2016, 14:15-15:15
- CMS MR13.
If you have a question about this talk, please contact Dr. J Ross. Given some class of “geometric spaces”, we can make a ring as follows. \begin{enumerate} \item[(i)] {\em (additive structure)} When $U$ is an open subset of such a space $X$, $[X] = [U] + [(X \setminus U)]$; \item[(ii)] (multiplicative structure) $[X \times Y] = [X] [Y]$. \end{enumerate} 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 is joint work with Melanie Matchett Wood. This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
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