Dear visgat & CART subscribers,
We are happy to announce that we will be holding a joint visgat/CART seminar on Oct 22nd, 2025 (Wed), 11:00 am - 12:00pm virtually and via Zoom. The seminar will be given by Veronica Kelsey (University of Manchester). The details are below:
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Date: Oct 22nd, 2025 (Wed) Time: 11:00am - 12:00pm Location: KIAS 1424 Zoom hybrid : https://kimsh.kr/vz
Title: Irredundant bases of permutation groups Abstract: A base of a group $G \leq \mathrm{Sym}(Omega)$ is a sequence $\Lambda$ of points in $\Omega$ such that the identity is the only element of $G$ fixing $\Lambda$ pointwise. The size of the smallest base is denoted $\mathrm{b}(G, \Omega)$. The study of bases dates back to the 19th century but perhaps their most important use has been in computational group theory. There is a large computational saving when $|\Lambda|<<|\Omega|$, and so we’d ideally like to know $\mathrm{b}(G, \Omega)$. Sadly there is no known efficient algorithm for finding these minimal bases, and Blaha showed in 1992 that determining $\mathrm{b}(G,\Omega) \leq c$ for a given constant $c$ is NP-complete. Instead we consider irredundant bases which can be thought of as the “best worst case”. In this talk I will introduce all these concepts along with examples and discuss some of the recent work in this area.
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After the seminar, we will head for lunch together. We would appreciate your interest!
Best wishes, Carl-Fredrik Nyberg-Brodda