

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. Skopenkov^{ab} ^{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
3dimensional 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 ntuples 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.

