Week 1 (Christina Grossack)

Introduction to Bott-Periodicity 

Bott periodicity is a fascinating subject at the intersection of topology,  homotopy theory, noncommutative algebra, and analysis. Few subjects can be so directly tied to such varied disciplines, and Bott periodicity (and the closely related K theory) is a rare gem that receives serious study from both (higher) category theorists and operator theorists. In this seminar, we'll study Bott periodicity from many different angles, and in this introductory talk we'll hopefully inspire interest in the subject, and very lightly sketch three very different proofs. Given time, we'll discuss generalized cohomology theories and hint at the relationship between Bott periodicity, K theory, and generalized cohomology.