Title (eng)

Nigel Higson: A rapid tour through noncommutative geometry - from integral equations and the spectral theorem to the index theorem and beyond


  Österreichische Zentralbibliothek für Physik


Mitschnitt eines Vortrags im Rahmen der Konferenz »Bivariant K-theory in Geometry and Physics« am Mittwoch, dem 21. November 2018 im Boltzmann-Hörsaal des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI)

Moderation: Bram Mesland (Max-Planck-Institut für Mathematik, Bonn)

Kamera und Schnitt: Daniel Winkler

Nigel Higson ist Professor für Mathematik an der Penn State University in University Park (Pennsylvania, USA).

Abstract: Hilbert’s theory of integral equations, now more than one hundred years old, is a famously successful amalgam of matrix algebra and analysis. One way to look at 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, and I shall try to develop this perspective in my lecture. I will focus on just one construction, that of Connes’ tangent groupoid, but even so there will be opportunities to glimpse at Weyl’s asymptotic law, the Atiyah-Singer index theorem, and recent work of Bismut on orbital integrals and the hypoelliptic Laplacian with v=0.


Kapitel Titel Position
1. Vorspann 00:00:00
2. Hilbert's spectral theorem 00:00:08
3. Integral operators as an algebra 00:09:06
4. Principal symbol 00:19:53
5. Two examples 00:29:29
6. The continuous field of C*-algebras 00:37:48
7. Elliptic operators 00:46:28
8. Bismut's theory of the hypoelliptic Laplacian 00:53:24
9. Questions from the audience 00:58:32

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