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Stephen McKean (Harvard University)

Tuesday, October 31
4:00 PM
203 TMCB

Title: Counting with quadratic forms

Abstract: Many theorems in enumerative geometry are restricted to algebraically closed fields. For example, a conic and cubic in the plane intersect 6 times over the complex numbers, but some of these intersections go missing over the reals. In this talk, I will discuss how to use tools from motivic homotopy theory to do enumerative geometry over arbitrary fields. Instead of integer-valued counts, these tools produce equations of quadratic forms. Invariants of these quadratic forms recover classical theorems from complex and real enumerative geometry and imply new theorems over other fields.