On the structure and statistics of the set of classical knots

• 主讲人：Andrei Malyutin (Saint Petersburg Department of Steklov Mathematical Institute)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-11-10 20:00 - 2022-11-10 21:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/8F9C3126AFDD066C5842C7AB0185D10B
Valid Until: 2026-12-31 23:59

 

Abstract: We study the structure and statistical characteristics of the set of classical knots. Particular points of this study are the statistics with respect to Thurston's classification (satellite/torus/hyperbolic) and the growth rates of the number of knots with respect to various complexity measures on the set of knots. New estimates for the growth rates of the number of prime knots with respect to the crossing number and arc index will be presented.

 

Bio: Andrei Malyutin is the deputy director of the Saint Petersburg Department of Steklov Mathematical Institute, a Professor at Saint Petersburg State University, having also an honorary degree of Professor of the Russian Academy of Sciences. He obtained his PhD in 2001 and got his Doctoral Degree (habilitation) in 2010. Andrey has some mathematical awards including the first prize in the International Mathematical Olympiad in 1992. His research interests include Geometric Topology, Geometric Group Theory, Dynamical Systems, Random Processes, etc. He provided solutions for a wide range of difficult problems, some of them going back to Markov and Poisson. Andrei is a member of the editorial board of several prestigious journals e.g. Algebra I Analiz.