Corneliu Hoffman (Birmingham): Spatchcoq-taming poultry, an approach to teaching proofs with computers (30 minutes)
I will present a software approach to teaching students how to write proofs. This is based on a bespoke customisable interface to Coq. For details ask me or see this repository. While it is not exactly discrete mathematics, most teaching examples are.
Sergey Kitaev (Strathclyde): Computational challenges in the theory of word-representable graphs (1 hour)
Encording graphs by words can be useful in solving problems on graphs. The much studied word-representable graphs can be encoded using alternation of letters in words. These graphs generalise several important classes of graphs such as 3-colorable graphs, combarability graphs, and circle graphs. Recognising word-representability is an NP-complete problem. One of the current computational challenges is enlaging the set of graphs whose non-word-representability can be verified by a human. Another computational direction is describing new subclasses of (non-)word-representable split graphs. Finally, yet another interesting direction from computational point of view is studying 12-representable graphs, a subclass of comparability graphs that includes permutation graphs and co-interval graphs.
Vince Knight (Cardiff): An open reproducible game theoretic framework (30 minutes)
In the 1980s Robert Axelrod carried out computer experiments that continue to be cited today as an explanation for the emergence of cooperative behaviour. I will discuss an open source piece of software that not only reproduced this but importantly (continues) to extend it.
Alexander Konovalov (St Andrews): CoDiMa CCP: 5 years on (1 hour) [slides]
An overview of community building and software maintenance activities being undertaken under CoDiMa CCP.
Steve Linton (St Andrews): meataxe64: a quick advert (15 minutes)
An overview of meataxe64 and a GAP package which provides low-level GAP bindings to use it from GAP.
Patrick Maier (Sheffield Hallam): Scaling parallel combinatorial search (30 minutes) [slides]
I will talk about YewPar a new C++ framework for parallel combinatorial search. The framework is suitable for scaling backtracking search/optimisation to large distributed compute clusters.
Dima Pasechnik (Oxford): On decomposing representations in charateristic 0 (30 minutes)
We discuss our exerience with implementing a classical decomposition method for representations of finite groups over C. We (re)discovered few interesting tricks to speed up seemingly very hard parts. Joint work with my student Kaashif Hymabaccus, who also implemented all this as GAP package decomp.
Sergey Shpectorov (Birmingham): Computing axial algebras (30 minutes)
Axial algebras are commutative non-associative algebras inherently related to groups. Examples include the Griess algebra for the Monster simple group and the classical Jordan algebras.
In 2013 I proposed an algorithm for computing axial algebras based on the concept of a partial algebra and an expansion. The initial version of the program was in GAP. However, later a more powerful MAGMA version was created by McInroy. This is mainly due to better linear algebra/group modules implementation in MAGMA. In the talk I’ll discuss the structure of the algorithm and the necessary operations, as well as a few ideas how the efficiency of the implementation can be improved.
Leonard Soicher (QMUL): Classifying the non-synchronizing primitive permutation groups (30 minutes) [slides]
The groups of the title are of interest to researchers in permutation groups, semigroups, and automata theory, and the current classification (up to degree 314) has required the development and use of new functionality in the GRAPE package for finding maximum cliques and proper vertex k-colourings, exploiting graph symmetry.
Chris Wensley (Bangor): Recent developments in packages XMod and Groupoids (30 minutes)
The talk will include: enumeration of cat2-group structures on a group; conversion between crossed squares and cat2-groups; crossed modules over groupoids; more general digraphs.
For the detailed schedule and further information, see this HackMD notepad for the workshop, where we will invite you to you to share organisational information and details about what you want to work on/have worked on during the workshop.