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SUMMARY:COW: Cutting and pasting in algebraic geometry - Ravi Vakil (Stanf
 ord)
DTSTART:20160421T131500Z
DTEND:20160421T141500Z
UID:TALK64811@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:Given some class of "geometric spaces"\, we can make a ring as
  follows.  \n\n\\begin{enumerate}\n\\item[(i)] {\\em  (additive structure)
 }  When $U$ is an open subset of such a space $X$\,  \n$[X] = [U] + [(X \\
 setminus U)]$\;\n\\item[(ii)] (multiplicative structure)  $[X \\times Y] =
  [X] [Y]$.\n\\end{enumerate}\n\nIn the algebraic setting\, this ring (the 
 "Grothendieck ring of varieties") contains surprising structure\, connecti
 ng geometry to arithmetic and topology.  I will discuss some remarkable st
 atements about this ring (both known and conjectural)\, and present new st
 atements (again\, both known and conjectural).  A motivating example will 
 be polynomials in one variable.  This is joint work with Melanie Matchett 
 Wood.
LOCATION:CMS MR13
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