## Top Global Course Special Lectures “Integral equations, the spectral theorem and an introduction to noncommutative geometry”

###
**Integral equations, the spectral theorem and an introduction to noncommutative geometry**
Prof. Nigel Higson

**Course Description**

Hilbert’s theory of integral equations, now over one hundred 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.

### Details

- Year/Term
- 2019

- Date
- June 20th, 2019

- Faculty/

Graduate School - Graduate School of Science

- Language
- English

- Instructor name
- Nigel Higson（Professor, Pennsylvania State University）

- Place
- Room 127, Graduate School of Science Bldg No 3

### Related Courses

**Basic Skills for Field Work non snow season (Ashiu Forest Research Station)**

Masae Ishihara, Yasuyuki Shibata

Graduate School of Science, Field Science Education and Research Center

2021**Top Global Course Special Lectures 2 “Spectrum of random graphs”**

Prof. Charles Bordenave

Graduate School of Science

2021**Top Global Course Special Lectures 1 “Loop space decompositions in homotopy theory with applications to Poincaré Duality spaces”**

Stephen Theriault

Graduate School of Science

2021**Vertex algebras, instanton counting and invariants of 3 and 4 dimensional manifolds**

Boris FEIGIN

Graduate School of Science

2019