# Plücker Lecture 2014

## *Prof. Dr. Nigel Higson, Penn State University*

*Prof. Dr. Nigel Higson, Penn State University*

**LECTURE 1: "****From Integral Equations to Noncommutative Geometry**"

**From Integral Equations to Noncommutative Geometry**"

Date: October 27, 4:30 PM.

Coffee will be served before the lecture.

The BIGS party will take place after the lecture!

**LECTURE 2: "****A Noncommutative View of Singular Spaces**"

**A Noncommutative View of Singular Spaces**"

Date: October 28, 4:30 PM.

Coffee and cake will be served before the lecture.

**LECTURE 3: "****Group Representations and Noncommutative Geometry**"

**Group Representations and Noncommutative Geometry**"

Date: October 29, 3:15 PM (which is the Hausdorff Colloquium).

Venue: Lipschitz-Room, Endenicher Allee 60

Abstract:

**Some Aspects of Noncommutative Geometry**

Hilbert's theory of integral equations is a famously successful amalgam of matrix algebra and analysis. One way of approaching Alain Connes' noncommutative geometry is to view it as an evolution of the theory of integral equations that incorporates new geometric ideas into Hilbert's work. I shall try to develop this perspective in these talks. In the first two lectures I shall introduce basic constructions that take the theory of integral equations quite far beyond its ordinary context, and then sketch some applications. In the last lecture, which will be more or less independent of the first two, I shall indicate some connections with Harish-Chandra-style representation theory.