Top Global Course Special Lectures by Prof. Nigel Higson (Pennsylvania State University) will take place as follows:

Date & Time

Thursday, June 20, 10:30-11:30

Venue

127 Conference Room, Faculty of Science Bldg. #3, Kyoto University

Title

Integral equations, the spectral theorem and an introduction to noncommutative geometry

Abstract

Hilbert's theory of integral equations, now over one handred years old, is a famously successful marriage of matrix algebra and analysis. One way to view Alain Connes' much newer noncommutative geometry is to see it as an evolution of the theory of integral equations that incorporates geometric ideas into Hilbert's work. I shall try to develop this perspective in my lecture. I will focus on one construction of Connes, which relates integral equations to Weyl's asymptotic law, the Atiyah-Singer index theorem, and more.

Language

English