Motivic Explorations in Enumerative Geometry - Part 3

Watch a mathematics lecture exploring how motivic homotopy theory enables enumerative geometry over arbitrary bases, providing deeper arithmetic and geometric insights. Delve into classic examples like Bézout's theorem and counting lines on cubic surfaces, examining solutions over complex and real numbers before generalizing to arbitrary fields using A1 degree from motivic homotopy theory. Learn about tropical geometry, particularly tropical plane curves, and their application in proving Bézout's theorem for curves over arbitrary fields. Explore tropical correspondence theorems from collaborative research with Jaramillo Puentes and ongoing work with Jaramillo Puentes-Markwig-Röhrle. Access accompanying lecture notes and problem sets to reinforce understanding of these advanced mathematical concepts within the broader context of the Graduate Summer School program on Motivic Homotopy Theory at PCMI.