An introduction to A^1 homotopy theory using enumerative examples - Kirsten Wickelgren

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PCMI 2021 Graduate Summer School

Topic: An introduction to A^1 homotopy theory using enumerative examples
Speaker: Kirsten Wickelgren
Affiliation: Duke University
Date: July 14, 2021
Wickelgren -2021-07-14

Abstract
Morel and Voevodsky's A^1 homotopy theory imports tools from algebraic topology into the study of schemes, or in other words, into the study of the solutions to polynomial equations. This theory produces greater understanding of arithmetic and geometric aspects these solutions. We will introduce some of this theory using as a guide questions such as "How many lines meet 4 lines in 3-space?"

Background: some algebraic topology or algebraic geometry, for example as described in Hatcher's and Hartshorne's books

  1. IAS | PCMI Park City Mathematics Institute
  2. Institute for Advanced Study
  3. IAS
  4. IAS/PCMI
  5. Park City
  6. Mathematics
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