# GTM seminar

Speaker: Jesse Wolfson (Northwestern University) Index Theory in Algebraic K-Theory and Algebraic Geometry Thu, Oct 10, 2013, 15:30 - 17:00 Seminar Room A 1038.pdf I will present a dictionary due to M. Sato which translates between the classical theory of Fredholm operators and the linear algebra of Tate vector spaces'' over arbitrary fields. I will explain how this dictionary produces counterparts in algebraic geometry to some of the key roles in differential topology of the theory of Fredholm operators. One of these roles is the Atiyah--Janich map Fred(\mathcal{H})\to\mathbb{K}^{top} which gives an equivalence between the space of Fredholm operators and (the infinite loop space representing) topological K-theory. I will describe recent work with O. Braunling and M. Groechenig which constructs a counterpart of this map for Tate spaces and algebraic K-theory, and I will sketch some of the applications this has allowed.