The Aharonov-Bohm effect and the Calderón problem for connection Laplacians large interaction problems

Leo Tzou
University of Helsinki and University of Sydney
27 August 2012 2-3pm, AGR Carslaw 829

Abstract

The Aharonov-Bohm effect is a quantum mechanical phenomenon where electrons passing through a region of vanishing magnetic field get scattered due to topological effects. It turns out that this phenomenon is closely related to the cohomology of forms with integer coefficients. We study this relationship from the point of view of the Calderón problem and see that it can be captured in how Cauchy data of the connection Laplacian determines uniquely the holonomy representation of the connection.

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