EVENT DETAILS AND ABSTRACT

Title: From matrices to motivic homotopy theory
Speaker: Aravind Asok
Speaker Info: USC
Brief Description:
Special Note:
Abstract:

From its inception in the now classical work of Cartan and Eilenberg and its development in the subsequent work of J.P. Serre and H. Bass, the theory of projective modules over a ring has drawn inspiration from the theory of vector bundles on topological spaces. I will survey some results explaining how the Morel-Voevodsky motivic homotopy theory has deepened the analogies between the two subjects and allowed one to establish new results that were completely out of reach of classical techniques. In particular, I will discuss recent joint work with Mike Hopkins and Tom Bachmann that allows one to completely resolve an old problem of M.P. Murthy.