Contractibility and Spheres: A Motivic View in Homotopy Theory

Explore fundamental concepts in motivic homotopy theory through a lecture that uses spheres and contractibility in topology as launching points for deeper algebro-geometric investigations. Join Professor Aravind Asok from the University of Southern California as he presents at the 2024 Program on Motivic Homotopy Theory at PCMI, delving into this powerful mathematical framework that emerged from Morel and Voevodsky's work in the 1990s. Learn how this field serves as both an essential tool for understanding arithmetic aspects in algebra and algebraic geometry, while also functioning as a fascinating generalization of classical homotopy theory. Gain insights into the intersection of algebraic geometry, algebraic topology, and homotopy theory, with additional context provided by Galois cohomology and étale cohomology concepts. Benefit from the collaborative environment of the Graduate Summer School at PCMI, where leading experts share their knowledge through carefully structured lectures and problem sessions designed to build practical understanding of complex mathematical concepts.