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# Tag Archives: oligomorphic permutation groups

## Oligomorphic groups: topology or geometry?

One perhaps unexpected result of the pandemic is that there is a huge volume of really interesting mathematics flying around the internet at the moment, courtesy of Zoom and other platforms. This week I went to a talk by Joy … Continue reading

## A counting problem

I quite often get questions by email. Mostly I can’t answer them, but sometimes I can, and sometimes the answers might be of more general interest. Suppose that we have m boxes and a supply of identical balls. In how … Continue reading

Posted in doing mathematics, exposition
Tagged balls in boxes, Cycle Index Theorem, oligomorphic permutation groups
1 Comment

## A crash course on group theory

I have just finished a crash course on group theory at Universidade de Lisboa. The notes are here. From the preface: On a visit to Universidade de Lisboa in November 2016, I was asked to give a “crash course” in … Continue reading

Posted in Lecture notes
Tagged Classification of Finite Simple Groups, finite groups, first-order logic, groups of prime power order, infinite groups, Jordan-Holder Theorem, locally finite groups, oligomorphic permutation groups, periodic groups, profinite groups, residually finite groups, Sylow's theorem, topology
1 Comment

## Banff, day 1

The first day of the meeting is over. We met in the well-appointed lecture room at BIRS, on the Banff Centre campus, with its comfortable seating: We have also had the group photo taken: The first day was devoted to … Continue reading

## Categorification, step 1

Today at the St Petersburg meeting, Igor Frenkel talked about categorification. He explained that there are five levels (maybe more!) and one has to take certain steps between them; he illustrated with an example, where level 0 was Jacobi’s Triple … Continue reading

## Eigen-species

The title of this post is half-serious: it is designed to catch attention, but I think there are interesting things lurking here which deserve more exploration. Species A species describes a class of objects built on finite sets, in a … Continue reading

Posted in exposition
Tagged binary trees, cographs, gorilla, N-free graphs, oligomorphic permutation groups, species
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