Index Theory for Beginners (Lecture 1)
Toshikazu Natsume (Nagoya Institute of Technology)
10:00-11:20, Dec 8, 2020 Zoom 467 658 1686
Abstract:
Section 1 : Motivation
Examples
History
Mystery in Geometry
Section 2: Functional Analysis, a quick review
Compact Operators
Fredholm Alternative
Fredholm Index
Section 3: Pseudodifferential Operators and Sobolev Spaces
Elliptic Operators
Parametrix
Section 4: The Atiyah-Singer-type Index Formulae
A Variant of A-S-type Index Formula for Rn
An Example worth investigating
Section 5: Developments
The Higson-Roe Index Theorem
Index Theorem appearing in Mathematical Physics
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