Analysis Seminar

Uniqueness problems for generalized quadrature domains with connections to Hele-Shaw flow and the Faber transform

Andrew Graven, Department of Mathematics, Caltech,

Classical quadrature domains (QDs) have been extensively studied over the last 60 years, yet little attention has been given to weighted QDs. I will discuss joint work with Prof. Nikolai Makarov on the extension of classical results for QDs to the weighted and Abelian cases, with the Faber transform being a key analytical tool. This includes a classification of one point QDs with respect to different weights. Furthermore, I will discuss the relationship between QDs, logarithmic potential theory, and Hele-Shaw flow. Finally, several concrete examples will be presented.
In the course of the presentation, the utility of the Faber transform for this class of problems will become apparent.

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For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit https://ucla.zoom.us/j/9264073849.