Many of our seminars are Pure Mathematics Colloquia, so why not check here?

## Previous CIRCA & Algebra Semigroups - 2015 to 2016

Previous Pure Mathematics Colloquia from: 2017/18, 2016/17, 2015/16, 2014/15, 2013/14, 2012/13, 2011/12, 2010/11, 2008/09, 2007/08**Wednesday the 15th of June 2016 at 4pm in Theatre D**

Casey Donoven
*University of St Andrews
***Comparing Equivalence Relations on Cantor Space
**

I will compare two types of relations on Cantor space that arise from fractal (self-similar) constructions. The first are known as invariant relations and are preserved under adding and removing common prefixes. The second are gluing relations formed from edge replacement systems. Both are associated with sequences of graphs, built from replacing vertices or edges with subgraphs, and I will describe the conditions necessary for them to be equivalent.

**Wednesday the 9th of March 2016 at 4pm in Theatre D**

Peter Cameron
*University of St Andrews
***Idempotent generation and road closures
**

With Joao Araujo, I have been looking at the following problem: which transitive permutation groups \(G\) on \(\{1,\ldots,n\}\) have the property that, for any map \(a\) whose image has size \(2\), the semigroup \(\langle G,a\rangle\setminus G\) idempotent generated? A naive algorithm for this takes exponential time, but we have a (probably) polynomial time algorithm to test a permutation group. It involves checking whether certain specified road closures in a vertex-primitive and edge-transitive road network disconnect the network. We have a nice conjecture about which groups satisfy the property, which we can prove one way round. One of the families of exceptions is related to the phenomenon of triality.

**Wednesday the 27th of January 2016 at 4pm in Theatre D**

Hugo Parlier
*University of Fribourg
***Puzzles, triangulations and moduli spaces
**

How does one measure distance between triangulations? What does the graph of the space of configurations of a Rubik’s cube look like? How do you enumerate domino tilings of a rectangle? These questions might not seem directly related but are all questions about the geometry of combinatorial moduli spaces. Starting from examples of spaces coming from puzzles, the talk will be about the geometry of different configuration spaces.