Venue: Conference Room 7.15, Level 7, Innova 21 building (see on the map).

Conference Poster

Abstract

Dirac introduced his eponymous operator to describe electrons in quantum theory. It was rediscovered by Atiyah and Singer in their study of the index problem on manifolds. In these lectures we explore new theorems and applications. Several of these also involve K-theory in its recent twisted and differential variations.


Titles of individual lectures

Loop groups and Dirac families
I will describe the finite and infinite-dimensional versions of the construction which yields my theorem with Hopkins and Teleman. This will include some generalities about loop groups and their representations.

Introduction to twisted K-theory
After a review of standard K-theory I will discuss the twisted form and some properties. Then I will compute twisted K_G(G) in some cases.

A TQFT from twisted K-theory
I will discuss TQFTs in general and give some examples, etc. I will show how to construct the ring structure on twisted K_G(G).

Differential K-theory and the Atiyah-Singer theorem
An introductory lecture on differential cohomology theories in general and differential K-theory in particular. Then the differential index theorem with Lott.

Anomalies and "categorified" index theorems
A general lecture on some physics, then some discussion of anomalies in supersymmetric quantum mechanics and on the worldsheet of string theory.

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