A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 2

Explore unstable motivic homotopy theory in this advanced mathematics lecture from the PCMI Graduate Summer School series. Delve into the Morel-Voevodsky category of motivic spaces, examine proofs of Morel's fundamental theorems on homotopy sheaves, and understand Morel's computation of first unstable homotopy sheaves of motivic spheres. Learn from Professor Joseph Ayoub of Universität Zürich as he builds upon the foundations laid in part 1, drawing from Morel's seminal work "A^1-algebraic topology over a field." While no prior knowledge of motivic homotopy theory is required, familiarity with basic algebraic geometry and algebraic topology concepts will enhance understanding of this 65-minute presentation. Access complementary lecture notes and problem sets to reinforce learning, as part of a comprehensive program that bridges classical homotopy theory with modern developments in algebra and algebraic geometry.