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# Category Archives: exposition

## Multifractal analysis

Yesterday, the Edinburgh Mathematical Society met in St Andrews. Thomas Jordan gave a talk on multifractal analysis. I had no idea what this was, and went along without too much expectation of being enlightened. But Thomas began with a well-chosen … Continue reading

Posted in exposition
Tagged Besicovich, Edinburgh Mathematical Society, Hausdorff dimension
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## Sum-free sets

This semester, Han Yu has run a reading group on Arithmetic Combinatorics. Mostly we have been following the excellent notes by Tuomas Orponen. I gave two talks. The first was a proof of the result of Ellenberg and Gijswijt on … Continue reading

Posted in exposition
Tagged Baire category, Calkin, density, Erdos, measure, Roth, Schoen, Schur, Szemeredi, van der Waerden
2 Comments

## The march of truth

You can find a thing I wrote about this on the Institute of Art and Ideas website at https://iainews.iai.tv/articles/the-march-of-truth-auid-788, as part of a “conversation” on The Limits of Reason.

## The ADE affair, 6

Earlier this semester, we had a beautiful seminar by Pierre-Philippe Dechant, whose work has thrown some entirely new light on this beautiful work of art. I would like to explain a bit about this here. For more details, see his … Continue reading

## Polynomials taking integer values

This is not a hot new result, just part of general mathematical culture. If a polynomial f(x) has integer coefficients, then its values at integer arguments are clearly integers. The converse is false; the simplest example is the polynomial x(x−1)/2. … Continue reading

Posted in exposition
Tagged difference polynomials, integers, polynomials, reciprocal polynomials
4 Comments

## Reciprocity

The cycle index of a finite permutation group is a multivariate polynomial (with one variable si for each index i not exceeding the degree of the group) which is the generating function for the numbers of cycles of different lengths … Continue reading

Posted in exposition
Tagged Bill Jackson, cycle polynomial, Jason Rudd, Jason Semeraro, orbital chromatic polynomial
1 Comment

## Two excursions

Last Friday, my friend Jan Kratochvil spoke to the Edinburgh Mathematical Society at the University of Stirling. I decided to go and hear him. The situation he talked about was typefied by this example. Suppose that you have a large … Continue reading

Posted in exposition, geography
Tagged Eildon Hills, geometric graphs, Jan Kratochvil, Ochil Hills, Stirling, Tweedbank
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