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# Category Archives: exposition

## Computational group theory, 1

Computational group theory is the art or science of using a computer to learn something about a group. I was introduced to it by John Cannon in the early 1980s. It seems like a black art to many mathematicians (myself … Continue reading

Posted in exposition
Tagged Bill Kantor, black-box group, Laszlo Babai, permutation group, presentation
1 Comment

## A celebration of diversity

Today, the University of Auckland put on a morning meeting entitled Excellence in Mathematics: A Celebration of Diversity. As the program (which is here) makes clear, it is actually a celebration of female mathematicians, and in particular the recent Fields … Continue reading

Posted in events, exposition
Tagged Fields medal, Lorenz surface, Maryam Mirzakhani, moduli spaces, optimality, relaxation time
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## Regular polytopes, 2

In the preceding post with this title, I showed how to translate the existence question for regular polytopes into one concerning groups, specifically string C-groups. I will begin by saying a bit more about the reverse construction. Suppose that we … Continue reading

## Regular polytopes, 1

One of the topics I am thinking about with Dimitri Leemans at present concerns regular polytopes. He and his co-authors Maria Elisa Fernandes and Mark Mixer have produced some nice results and a tantalising problem about these objects. I will … Continue reading

## A symmetric design

Quite a long time ago, Arunas Rudvalis discovered a symmetric 2-(14080,1444,148) design: a set of 14080 points, with 14080 subsets of size 1444 called blocks, with the property that any point lies in 1444 blocks, any two points in 148 … Continue reading

Posted in doing mathematics, exposition
Tagged Arunas Rudvalis, Cheryl Praeger, GAP, Symmetric design
2 Comments

## A cliff

The “combinatorial explosion” is a well-known phenomenon. I recently came across a very dramatic example of it. I was trying to compute the function F(n,k), defined to be the maximum of |S|×|P|, over all sets S of k-subsets and all … Continue reading

Posted in exposition
Tagged combinatorial explosion, computers, GAP, GRAPE, Leonard Soicher, partitions, subsets, transversals
4 Comments

## Groups, lattices and bases

About ten years ago I wrote a six-page paper, which I didn’t succeed in getting any journal editor to publish. I will say a bit about its contents below, but you can read it now: I have posted it on … Continue reading