Spectral asymptotics for coupled Dirac operators
Name
828406290-MIT.pdf
Description
Full printable version
Size
5.14 MB
Format
Adobe PDF
Checksum (MD5)
51fc0141c37a43e6f46ab09dd26f4328
Author(s)
Savale, Nikhil, Jr. (Nikhil A.)
Advisor(s)
Tomasz Mrowka.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we study the problem of asymptotic spectral flow for a family of coupled Dirac operators. We prove that the leading order term in the spectral flow on an n dimensional manifold is of order r n+1/2 followed by a remainder of O(r n/2). We perform computations of spectral flow on the sphere which show that O(r n-1/2) is the best possible estimate on the remainder. To obtain the sharp remainder we study a semiclassical Dirac operator and show that its odd functional trace exhibits cancellations in its first n+3/2 terms. A normal form result for this Dirac operator and a bound on its counting function are also obtained.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 137-139).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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