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홈 > 학술정보 >학술행사 > 세미나
KAIST 수리과학과 세미나

Title
[CMC 정오의 수학산책] Atiyah-Singer index theorem
Speaker
이윤원   (인하대 )
Date
2017-04-28 12:00:00
Host
KAIST
Place
자연과학동(E6-1) Room 3435
Abstract
The Atiyah-Singer Index Theorem appeared in 1960’s, which is one of great mathematical achievements in 20th century. It is a far reaching generalization of the Gauss-Bonnet-Chern Theorem for the Euler characteristic, the Hirzebruch Signature Theorem for the Signature of 4k-dimensional compact manifold, the Riemann-Roch-Hirzebruch Theorem for the Arithmetic Genus. Hence to understand this magnificent theorem, we need to investigate how the Euler characteristic, Signature and Arithmetic Genus are expressed by the Fredholm Indices for some appropriate geometric operators. In this talk, I will explain briefly the historical background of the Index Theorem, the Fredholm Indices of elliptic operators and discuss how the Index Theorem was motivated from the above classical celebrated theorems. And then, I will go through very briefly the proof of the Index Theorem by using the heat kernel method. If time permits, I will explain the Index Theorem on a compact manifold with boundary, where the eta-invariant appears as a boundary correction term.
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