Finite point configurations in discrete and continuous settings

Abstract: We are going to discuss the following basic question. How large does a subset of a given vector space need to be to ensure that it contains vertices of a finite point configuration of a given type, such as an equilateral simplex or a long chain? In the finite setting, the size is usually measured in terms of the number of points. In the continuous setting, the Hausdorff dimensions play this role. These types of questions have been studied intensively over the years by people like Bourgain Erdos, Du, Falconer, Furstenberg, Guth, Katz, Katznelson, Lyall, Magyar, Mattila, Ou, Rudnev, Shmerikin, Szemredi, Tao, Wang, Weiss, Zhang, and many others. We are going to survey the known results with an emphasis on the interaction of techniques and ideas from different areas of mathematics.

Mathematics

Audience: general audience

( video )

Comments: Please notice the updated start time. The talk will now start 30 min before it was earlier announced.

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Yerevan Mathematical Colloquium

Series comments: "Yerevan Mathematical Colloquium" invites survey talks aimed at a general mathematical audience, that emphasize proof methods, relations between branches of mathematics, possible applications, and open problems.

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