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

## Previous CIRCA & Algebra Semigroups - 2016 to 2017

Previous Pure Mathematics Colloquia from: 2016/17, 2015/16, 2014/15, 2013/14, 2012/13, 2011/12, 2010/11, 2008/09, 2007/08

Wednesday the 19th of April 2017 at 4pm in Lecture Theatre D

Heriot-Watt University
Plants, languages and groups

In the 1960s Lindenmeyer introduced a class of grammars and languages, called L systems, whose goal was to model the growth of plants and other organisms. It turns out that these languages also describe lots of important sets that naturally occur in group theory. The set of primitive words in the free group of rank two, the solutions sets of equations in free groups, normal forms for fundamental groups of 3-manifolds, or the words that represent non-trivial elements in the Grigorchuk group, are all examples of L systems.

In this talk I will give all the language definitions, and discuss as many of the examples above as time will allow.

Wednesday the 12th of April 2017 at 1pm in Theatre D

Ewa Bieniecka, Daniel Bennett, and Feyisayo Olukoya
University of St Andrews

Ewa Bieniecka

Title: Free products in R. Thompson’s group V

Abstract: Historically an approach to showing a group of permutations factors as a free product of its subgroups is to show the existence of “Ping-Pong” dynamics. However, it is the case that one can find permutation groups which factor as free products but without Ping-Pong dynamics. In recent years it has become a question as to whether any free product of subgroups of V admits Ping Pong dynamics in its natural action on Cantor space. In this talk we discuss some results related to this question. Joint work with Collin Bleak and Francesco Matucci.

Daniel Bennett

Title: An introduction to a class of co-context free Thompson-like groups

Abstract: In 2014 Witzel and Zaremsky introduced new Thompson-like groups based on the Zappa-Szép product of monoids. It was subsequently shown by Berns-zieve, Fry, Gillings, Hoganson and Mathews that a class of these groups, $$V_{aug}$$, had the property of being co-context free. We present a brief exploration of these groups and our work involved in attempting to use the groups as counter examples to Lehnert’s conjecture for V.

Feyisayo Olukoya

Title: The rational group and some of its subgroups

Abstract: I will give a brief introduction to the rational group, highlight some of its interesting subgroups and note along the way some results about these subgroups.

Wednesday the 5th of April 2017 at 1pm in Lecture Theatre D

John Gimbel
A few parameters in fractional graph theory

Many branches of mathematics have seen so called fractional reinterpretations of their discipline. E.g. Fractional geometry and fractional calculus. This talk is meant as a gentle introduction to fractional graph theory. In doing so, we will consider several parameters--domination, coloring and cocoloring and their fractional counterparts.

Wednesday the 8th of March 2017 at 1pm in Theatre D

Tomas Nilson
Mid-Sweden University
Agrawal’s conjecture for triple arrays

A triple array is an array in which two 2-designs are merged together such that any row and column contain the same number of common symbols.

Agrawal’s conjecture says that (in the canonical case), there is a triple array if and only if there is a symmetric 2-design (SBIBD).

Given a triple array we can construct a SBIBD. But here we will look at approaches and problems surrounding the desirable and still open direction. How to construct an array with these properties from a subset structure.

We will give background and define objects used. The exposition will be elementary and special knowledge of the area will not be assumed.

Friday the 24th of February 2017 at 2pm in Lecture Theatre A

Robert Bailey
Memorial University of Newfoundland
Metric dimension, computation and distance-regular graphs