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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
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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, firstorder logic, groups of prime power order, infinite groups, JordanHolder Theorem, locally finite groups, oligomorphic permutation groups, periodic groups, profinite groups, residually finite groups, Sylow's theorem, topology
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Banff, day 1
The first day of the meeting is over. We met in the wellappointed 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
Eigenspecies
The title of this post is halfserious: 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, Nfree graphs, oligomorphic permutation groups, species
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