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Analysis and PDE

Analysis Seminar: Alexander Vasiliev

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Speaker: Alexander Vasiliev, Professor, Mathematical Department, UiB.

Title: Analysis and topology of polynomial lemniscates II.

Abstract: We continue with the second topological part of the seminar. The first part of my talk is dedicated to fingerprinting polynomial lemniscates. It turns out that they represent a good tool of image analysis and can be used for approximation of planar shapes. We study their fingerprints (in Mumford's terminology) by conformal welding and reveal the geometric sense of their inflection points. The second part concerns with the topological aspects of lemniscates. In particular, they perform the structure of an operad.