A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 3

Explore unstable motivic homotopy theory in this advanced mathematics lecture, the third part of a series on A^1-algebraic topology presented by Joseph Ayoub from Universität Zürich. 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. While no prior knowledge of the specific subject is required, benefit from having a foundation in basic algebraic geometry and algebraic topology concepts. Access complementary lecture notes and problem sets to reinforce learning of this sophisticated mathematical theory that bridges classical homotopy theory with arithmetic aspects of algebra and algebraic geometry. Part of the 2024 Graduate Summer School program at PCMI, this lecture contributes to a broader series of minicourses taught by field experts, featuring daily problem sessions and opportunities to interact with researchers across various levels in the field.