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Loewner-Kufarev Evolutions

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If you have a question about this talk, please contact Alexis Marchand .

Loewner-Kufarev Evolutions are a representation for (continuously) growing simply connected sets in the plane. To my knowledge it is one of the very rare analytic representation theorems. The core idea is that we can describe growing sets by a family of measures that encodes how quickly which part of the boundary grows. As a result, we obtain an equivalence between analytic properties of certain functions and geometric properties of simply connected sets in the plane. This approach has been applied to prove distortion estimates of conformal maps and is very popular in studying random growth models.

This talk is part of the Junior Geometry Seminar series.

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