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# Category Archives: doing mathematics

## Automorphism groups of transformation semigroups

I have been in the transformation semigroups game for nearly ten years now, but I still feel that I am finding my feet. Here is apparently a huge difference between permutation groups and transformation semigroups, one which is still not … Continue reading

Posted in doing mathematics, open problems, Uncategorized
Tagged automorphism, primitive groups, synchronization
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## Prospects in Mathematics, 2

I didn’t say anything about my own talk at the Prospects in Mathematics meeting. But soon afterwards I was re-reading Lee Smolin’s 2006 book The Trouble with Physics, and it resonated with some of the things I said. My topic … Continue reading

Posted in doing mathematics, events
Tagged CFSG, Classification of Finite Simple Groups, Lee Smolin, string theory
7 Comments

## Perth, week 1

The first week of the visit is over. The weather has been quite cold, but it is likely to improve as time goes on. The best day so far was yesterday, when we went to Yanchep National Park and had … Continue reading

Posted in doing mathematics, exposition
Tagged derangements, H. Zantema, Jordan's theorem
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## More groups

The title reminds me of the occasion when my academic grandfather lectured to the London Mathematical Society on “Moore graphs”. Unfortunately, someone got it wrong, and his lecture was billed as “More graphs”. But here I really do mean what … Continue reading

## 12160

12160 is an interesting number; but I didn’t know that until last night. As part of the work on semigroups, we are looking at the following problem. Given n and k, with n ≥ 2k, suppose that G is a k-homogeneous subgroup … Continue reading

Posted in doing mathematics, exposition
Tagged 4-homogeneous, permutation groups, semigroups
3 Comments

## An Aveiro theorem

When I was a child, one of the radio serials we listened to was The Lone Ranger. Typically, when the Lone Ranger with his sidekick Tonto had cleared up another mess of wrongdoing or whatever, he would say to Tonto, … Continue reading

## Open science again

Just after my three pieces on open science (covering open publication, data, and software) was published on the CoDiMa blog, a message came round telling us to do something about ResearchFish. This, if you are fortunate enough not to have … Continue reading