Motivic Explorations in Enumerative Geometry - Part 4

Explore advanced mathematical concepts in a lecture focusing on motivic homotopy theory's applications in enumerative geometry, delivered by Sabrina Pauli from Technische Universität Darmstadt. Delve into how motivic homotopy theory enables enumerative geometry calculations over arbitrary bases, yielding valuable arithmetic and geometric insights. Learn about essential tools for solving enumerative geometry problems, including tropical geometry applications. Examine classic examples like Bézout's theorem and the counting of lines on cubic surfaces, first through the lens of complex and real numbers, then expanding to arbitrary fields using A1 degree from motivic homotopy theory. Study tropical plane curves and their role in proving Bézout's theorem for curves over arbitrary fields, concluding with discussions on tropical correspondence theorems from collaborative research. Access comprehensive lecture notes and problem sets to reinforce understanding of these advanced mathematical concepts, suitable for students with foundational knowledge in algebraic geometry, algebraic topology, and homotopy theory.