Rectangular diagrams of links, surfaces, and foliations

• 主讲人：Ivan Dynnikov (Steklov Mathematical Institute of RAS, MSU)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2025-04-10 21:00 - 2025-04-10 22:00
• 地点： Online

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Recording: https://meeting.tencent.com/dm/LisB1icKvvyu

 

Abstract: The formalism of rectangular diagrams provides a convenient framework for representing links and surfaces in the three-sphere in a consistent manner. They appear to have a strong connection with contact topology, as well as nice combinatorial properties, which make them useful for solving algorithmic and classification problems of knot theory. In particular, they allow to construct a simple algorithm for recognizing the unknot and to solve the problem of algorithmic classification of Legendrian and transverse links. One can also use rectangular diagrams to obtain explicit presentations of finite depth taut foliations in link complements.

 

Bio: Ivan Alekeevich Dynnikov is a leading researcher at Steklov Mathematical Institute and a professor of Moscow State University and a worldwide known expert in geometry and topology. His research interests include low-dimensional topology, dynamical systems, graph theory, mathematical physics, foliations, braid theory and knot theory. He has received his DS/Habilitation degree in 2007 and a honorable degree of Professor of Russian Academy of Sciences in 2016.

Prof. Dynnikov solved several famous problems, for instance:

- he constructed a monotone simplification algorithm for recognizing a trivial knot;

- proved Jones's conjecture (jointly with M. V. Prasolov);

- solved S. P. Novikov's problem on plane sections of 3-periodic surfaces;

- constructed a new discrete analogue of a complex structure on a plane (jointly with S. P. Novikov).