Algebra & Combinatorics Seminars
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Previous Seminars - 2019 to 2020

Previous seminars from: 2019/20, 2018/19, 2017/18, 2016/17, 2015/16, 2014/15, 2013/14, 2012/13, 2011/12, 2010/11, 2008/09, 2007/08

Wednesday 9 October at 1:00pm in Lecture Theatre D

Peter Cameron
University of St Andrews
Growth rates for oligomorphic groups

A permutation group \(G\) on an infinite set \(\Omega\) is oligomorphic if the number \(f_n(G)\) of \(G\)-orbits in its induced action on the \(n\)-element subsets of \(\Omega\) is finite for all positive integers \(n\).

Oligomorphic groups are essentially the same as automorphism groups of countably categorical first-order structures.

In the 1980s I started investigating these, and found what appeared to be a detailed structure of gaps in the growth rates. Apart from some very nice results by Dugald Macpherson, not much was done until very recently. But in the last year or two, many of my conjectures have been proved by Justine Falque, Nicolas Thiéry, Pierre Simon and Samuel Braunfeld. The techniques were algebraic (Cohen--Macauley algebras) and model-theoretic (monadic stability).

Wednesday the 2nd of October at 1.00pm in Lecture Theatre D

Louis Theran
University of St Andrews
Unlabelled distance geometry

In the 1930’s Schönberg and Young-Householder classified when \(\binom{n}{2}\) numbers \(m_{ij}\) are the pairwise distances among n points \(p_1, …, p_n\) in a Euclidean space and showed how to find the points from the distances. This question of finding the points becomes more difficult when you take away the association between the \(m_{ij}\) and the points \(p_i\), but it was solved by Boutin and Kemper in the mid 2000’s. I’ll talk about some generalisations of Boutin and Kemper’s results obtained jointly with Shlomo Gortler and Dylan Thurston and Ioannis Gkioulekas, Shlomo Gortler, and Todd Zickler.