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Mathematical Physics Seminar

A localization result for Dirac operators

Manousos Maridakis: Rutgers University

Location:  Hill 705
Date & time: Thursday, 16 February 2017 at 12:00PM - 12:11PM

The symbol map of a Fredholm Operator is carrying essential topological and geometrical information about the underline manifold. In this talk we study Dirac type operators involving a perturbation term. In particular we think of operators of the form \[{cal D} + s{cal A} :Gamma(E)ightarrow Gamma(F)\]over a Riemannian manifold \[(X, g)\]for special bundle maps \[{cal A} : Eightarrow F\]and study their behavior as \[sightarrow infty\]. There are two main aspects of localization being examined: First is the separation of the spectrum of this family of operators into low and high eigenvalues for large \[s\]. Second is the observation that eigenvectors corresponding to low eigenvalues \[L^2\]concentrate near the singular set of the perturbation bundle map \[{cal A}\]. This gives a new localization formula for the index of \[D\]in terms of the singular set of \[{cal A}\].

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