Worrying news from Turkey

One should of course be concerned when anybody is detained for spurious reasons, but when that person is a noted mathematician, the shock is greater. Six academics have recently been detained in Turkey, of whom one, Betül Tanbay, is due to become vice president of the European Mathematical Society in January. I do not know of any petitions for their release, but if they are not released very quickly I hope that there will be a strong reaction. The EMS has issued the following statement.

The European Mathematical Society is outraged at the news that the Turkish police have detained, in Istanbul on the morning of 16th November 2018, Professor Betül Tanbay, a member of the EMS Executive Committee. We are incredulous at the subsequent press release from the Istanbul Security Directorate accusing her of links to organized crime and attempts to topple the Turkish government.

Professor Tanbay is a distinguished mathematician and a Vice President Elect of the European Mathematical Society, due to assume that role from January 2019. We have known her for many years as a talented scientist and teacher, a former President of the Turkish Mathematical Society, an open-minded citizen, and a true democrat. She may not hesitate to exercise her freedom of speech, a lawful right that any decent country guarantees its citizens, but it is preposterous to suggest that she could be involved in violent or criminal activities.

We demand that Professor Tanbay is immediately freed from detention, and we call on the whole European research community to raise its voice against this shameful mistreatment of our colleague, so frighteningly reminiscent of our continent’s darkest times.

Update. I have just seen this on Twitter:

Police freed 8 people, incl. professors Turgut Tarhanli and Betul Tanbay, while barring them from overseas travel, & is still questioning 6 others

A quasirandomness implication

This is a bit of a niche post, since its target audience is people who are familiar with quasirandom graphs and like proofs of an analytic flavour. Very roughly, a quasirandom graph is one that behaves like a random graph of the same density. It turns out that there are many ways that one can interpret the phrase “behaves like a random graph” and, less obviously, that they are all in a certain sense equivalent. This realization dates back to seminal papers of Thomason, and of Chung, Graham and Wilson.

I was lecturing on the topic recently, and proving that certain of the quasirandomness properties all implied each other. In some cases, the proofs are quite a bit easier if you assume that the graph is regular, and in the past I have sometimes made my life easier by dealing just with that case. But that had the unfortunate consequence that when I lectured on Szemerédi’s regularity lemma, I couldn’t just say “Note that the condition on the regular pairs is just saying that they have quasirandomness property ” and have as a consequence all the other quasirandomness properties. So this year I was determined to deal with the general case, and determined to find clean proofs of all the implications. There is one that took me quite a bit of time, but I got there in the end. It is very likely to be out there in the literature somewhere, but I haven’t found it, so it seems suitable for a blog post. I can be sure of at least one interested reader, which is the future me when I find that I’ve forgotten the argument (except that actually I have now found quite a conceptual way of expressing it, so it’s just conceivable that it will stick around in the more accessible part of my long-term memory).