2026-09-19T08:31:18Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/778042022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Tomasz Mrowka.
Savale, Nikhil, Jr. (Nikhil A.)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2013-03-13T15:49:00Z
2013-03-13T15:49:00Z
2012
2012
http://hdl.handle.net/1721.1/77804
828406290
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 137-139).
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.
by Nikhil Savale.
Ph.D.
139 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Spectral asymptotics for coupled Dirac operators
Thesis
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Publication
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