$A^1$ enumerative geometry: counts of rational curves in $P^2$ - 1 of 2

Speaker: 
Kirsten Wikelgren
Date: 
Tue, Jun 11, 2019
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Arithmetic Topology
Abstract: 

We will introduce $A^1$ homotopy theory, focusing on the $A^1$ degree of Morel. We then use this theory to extend classical counts of algebraic-geometric objects defined over the complex numbers to other fields. The resulting counts are valued in the Grothendieck--Witt group of bilinear forms, and weight objects using certain arithmetic and geometric properties. We will focus on an enrichment of the count of degree $d$ rational plane curves, which is joint work with Jesse Kass, Marc Levine, and Jake Solomon.

 



This is the first lecture in a two part series: part 2

Class: