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

Date
2019/06/20 Thu 10:30 - 11:30
Room
127 Conference Room, Building No.3
Speaker
Nigel Higson
Affiliation
Pennsylvania State University
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.

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