From Matrices to Motivic Homotopy Theory

Explore fundamental concepts in motivic homotopy theory through this graduate-level lecture delivered at the PCMI Park City Mathematics Institute by Professor Aravind Asok from the University of Southern California. Part of the 2024 Graduate Summer School program focused on Motivic Homotopy Theory, learn how this mathematical framework emerged from Morel and Voevodsky's work in the 1990s and has evolved into a powerful tool for understanding arithmetic aspects in algebra and algebraic geometry. Delve into topics including unstable motivic homotopy theory, characteristic classes in stable motivic homotopy theory, applications in enumerative geometry, and connections to Weil conjectures. Gain insights from this comprehensive program designed for students with foundational knowledge in algebraic geometry, algebraic topology, and homotopy theory, with additional background in Galois cohomology and étale cohomology being beneficial. Benefit from the collaborative learning environment of PCMI, featuring daily problem sessions and interactions with researchers across various levels in the field.