A¹-Algebraic Topology and Introduction to Unstable Motivic Homotopy Theory - Part 1

Explore the first lecture in a series on unstable motivic homotopy theory, delivered by Joseph Ayoub from Universität Zürich at the IAS PCMI Park City Mathematics Institute. Delve into the foundations of the Morel-Voevodsky category of motivic spaces, examining Morel's fundamental theorems on homotopy sheaves and his computation of first unstable homotopy sheaves of motivic spheres. While no prior knowledge of motivic homotopy theory is required, gain more from the lecture with a background in basic algebraic geometry and algebraic topology concepts. Access complementary lecture notes and problem sets to reinforce understanding of this mathematical field that emerged from Morel and Voevodsky's work in the 1990s, serving as both a powerful tool for understanding arithmetic aspects in algebra and algebraic geometry, and a fascinating generalization of classical homotopy theory.