# Algorithms and Software for Discrete Computational Mathematics

Website of the workshop : https://circa-standrews.github.io/codima2019workshop/

Minutes of the workshop: https://hackmd.io/s/ryZX827a4

# Thursday May 23rd

9:30 - 10:00 : Coffee on arrival
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10:00 - 10:30 : Welcome
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Welcome
- Housekeeping:
- using HackMD for minutes
- minutes are at https://hackmd.io/s/ryZX827a4
- expenses claims
- laptop stickers!
- Round of introductions
- Plan for today

10:30 - 11:00
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- CoDiMa CCP overview (Alexander Konovalov)
- Part 1: Community building
- workshops
- training events
- networking activities

11:00 - 11:30 : Coffee break
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11:30 - 12:00
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- CoDiMa CCP overview (Alexander Konovalov, continued)
- Part 2: Software development
- GAP release management
- New features in recent GAP releases
- State of the GAP packages ecosystem

12:00 - 12:30
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- Dima Pasechnik, *On decomposing representations in charateristic 0*

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 https://gitlab.com/kaashif/decomp

12:30 - 14:00 : Lunch
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14:00 - 15:30
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- Discussion: CoDiMa CCP - Phase two
- see separate notes at https://hackmd.io/s/rJ9A7scnE
- Potential flagship software development projects

15:30 - 16:00 : Coffee break
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16:00 - 17:00
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- Discussion: CoDiMa CCP - Phase two (continued)
- see separate notes at https://hackmd.io/s/rJ9A7scnE
- Potential flagship software development projects
- Wrapping up and making the plan for tomorrow

17:00 - 18:00
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- Drinks at sandbar: http://sandbarmanchester.co.uk/

18:00
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- Dinner at Samsi https://www.samsi.co.uk/

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# Friday May 24th

Start at 9:00
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## Further research talks (schedule to be determined):

Please tell us about interesting research problems which hopefully could be solved using computational techniques, or report about research carried out using mathematical software. Add your name, the title of your talk, and a short (a couple of sentences) abstract below.

- Sergey Kitaev, *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.

- Leonard Soicher, *Classifying the nonsynchronizing primitive permutation groups* (30 minutes)
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, *Recent developments in packages XMod and Groupoids* (30 minutes)
To include: enumeration of cat2-group structures on a group; conversion between crossed squares and cat2-groups; crossed modules over groupoids; more general digraphs.

- Vince Knight, *An open reproducible game theoretic framework* (20 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.

- Corneliu Hoffman, *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 http://spatchcoq.co.uk/spatchcoq. While it is not exactly discrete mathematics, most teaching examples are.

- Patrick Maier, *Scaling parallel combinatorial search* (20 minutes)
I will talk about [YewPar](https://github.com/BlairArchibald/YewPar) a new C++ framework for parallel combinatorial search.
The framework is suitable for scaling backtracking search/optimisation
to large distributed compute clusters.

- Sergey Shpectorov, *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.

- https://mwhybrow92.github.io/MajoranaAlgebras/

## Discussions:
- CoDiMa - phase two: see separate notes at https://hackmd.io/s/rJ9A7scnE
- Potential flagship software development projects

## Schedule guildelines

09:00 : Start
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Vince Knight
Corneliu Hoffman
Chris Wensley

11:00 - 11:30 : Coffee break
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11:30 - 12:30
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Sergey Kitaev

12:30 - 14:00 : Lunch
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Steve Linton
Sergey Shpectorov
Leonard Soicher

14:00 - 15:30
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15:30 - 16:00 : Coffee break
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Patrick Maier

17:00 : Finish
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## Saturday May 25th : Hackday (09:30 - 15:00)

Please list here activities on which you would like to work during the hackday
- Alexander Konovalov: work with Sasha Borovik on https://github.com/sukru-yalcinkaya/unipoly
- Leonard Soicher: work on a C front-end to my coset enumerator (Q: *is your coset enumerator available to the public? Dima*.)
- Making a questionnaire to gather community feedback

Starting notes for the questionaire at https://hackmd.io/AL5ojSC4RTWJjwVPTmB09A

## Housekeeping

Coffee breaks:

- 9.30 am on arrival on Thursday
- 11 am on Thursday and Friday
- 3.30 pm on Thursday and Friday

Lunches:
- Sasha will be leading us to some place nearby

On Saturday there will be no coffee supplied to the room, so we advise to buy it elsewhere.