Motivic Explorations in Enumerative Geometry - Part 1

Explore a comprehensive lecture on motivic homotopy theory's applications in enumerative geometry through this graduate-level mathematics presentation. Delve into classic examples like Bézout's theorem and the counting of lines on cubic surfaces, examining solutions over complex and real numbers before extending to arbitrary fields using A1 degree from motivic homotopy theory. Learn about tropical geometry with a focus on tropical plane curves and their role in proving Bézout's theorem for curves over arbitrary fields. Discover tropical correspondence theorems from collaborative research with Jaramillo Puentes and ongoing work with Jaramillo Puentes-Markwig-Röhrle. Access supplementary materials including detailed lecture notes and problem sets to reinforce understanding of these advanced mathematical concepts. Part of the 2024 Graduate Summer School program at PCMI, this lecture assumes foundational knowledge in algebraic geometry, algebraic topology, and homotopy theory.