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Iskovskikh Seminar
April 16, 2015 19:00, Moscow, Steklov Mathematical Institute, room 540
 


Surfaces containing several circles through each point (on a joint work with R. Krasauskas)

M. B. Skopenkovab

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University "Higher School of Economics", Moscow

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Abstract: Motivated by potential applications in architecture, we study surfaces in 3-dimensional Euclidean space containing several circles through each point. Finding all such surfaces is a challenging open problem. We provide some bright examples and reduce the problem to a nice algebraic problem of finding Pythagorean n-tuples of polynomials.
Our main tools is a generalization of the Schicho theorem on the parametrization of the surfaces containing two conics through each point. We are going to state and prove several lemmas to the theorem.
A substantial part of the talk is elementary and is accessible even for high school students. Several open problems are stated.

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