主 讲 人 ：Grigory Ryabov    副教授

活动时间：2025-06-05 18:00:00

地      点 ：理科群1号楼D203室 https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1 会议 ID: 86763384947；密码: 612593

主办单位：数学科学学院

讲座内容：

An (association) scheme is said to be \emph{Frobenius} if it is the orbital scheme of a Frobenius group. A scheme which has the same tensor of intersection numbers as some Frobenius scheme is said to be pseudofrobenius.

We establish a necessary and sufficient condition for an imprimitive pseudofrobenius scheme to be Frobenius. We also prove strong necessary conditions for the existence of an imprimitive pseudofrobenius scheme which is not Frobenius. As a byproduct, we obtain a sufficient condition for an imprimitive Frobenius group $G$ with abelian kernel to be determined up to isomorphism only by the character table of $G$. Finally, we prove that the Weisfeiler-Leman dimension of a circulant graph with $n$ vertices and Frobenius automorphism group is equal to $2$ unless $n \in \{p, p^2, p^3, pq, p^2q\}$, where $p$ and $q$ are distinct primes. The talk is based on the results from [Ponomarenko and Ryabov, Journal of Algebraic Combinatorics 57 (2023),  No. 2, 385-402].

主讲人介绍：

Grigory Ryabov holds a Ph.D. in Mathematics from the Sobolev Institute of Mathematics and Novosibirsk State University (Novosibirsk, Russia). He has held postdoctoral research positions at the St.\ Petersburg Department of the V.A.~Steklov Institute of Mathematics (St. Petersburg, Russia) and at Ben-Gurion University of the Negev (Be'er-Sheva, Israel), as well as a senior research fellowship at the Sobolev Institute of Mathematics (Novosibirsk, Russia). Currently, he serves as an associate professor at Novosibirsk State Technical University (Novosibirsk, Russia) and as a visiting associate professor at Hebei Normal University (Shijiazhuang, China).

He is the author or co-author of 27 research papers, some of which have appeared in leading international journals such as Journal of Combinatorial Theory, Series A, Journal of Algebraic Combinatorics, Designs, Codes and Cryptography, and Discrete Mathematics. His main research interests lie at the intersection of algebra and combinatorics.