# Seminars & Colloquia Calendar

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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