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Around Tao’s algebraic regularity lemma


School of Mathematical Sciences

About the Project

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2020 for self-funded students.

This project will be supervised by Dr Ivan Tomasic.

Everybody is talking about Tao’s algebraic regularity lemma. In every area of mathematical research, from (algebraic) combinatorics, model theory (logic), number theory and algebraic geometry, researchers are finding new and inventive ways of using it and finding new instances and analogues of it.

In short, Tao’s regularity lemma is a variant of the celebrated Szemeredi’s regularity lemma (which is a result for arbitrary graphs) that works for graphs that can be defined over the so-called pseudofinite fields (or uniformly over finite fields). It says that such a graph can be decomposed into pieces roughly about the same size so that the edges between those pieces behave almost randomly.

For more information, please see here: https://www.qmul.ac.uk/maths/media/maths/postgraduate/phd-projects/Tomasic_2020.pdf

The application procedure is described on the School website. For further inquiries please contact Dr Ivan Tomasic at .

Funding Notes

This project can be undertaken as a self-funded project. Self-funded applications are accepted year-round for a January, April or September start.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.

References

[1] Mirna Dzamonja and Ivan Tomasic. Graphons arising from graphs de finable over fi nite fi elds. https://arxiv.org/abs/1707.06296

[2] Anand Pillay and Sergei Starchenko. Remarks on Tao's algebraic regularity lemma. http://www3.nd.edu/~apillay/papers/regularitylemma.pdf

[3] Terrence Tao. Expanding polynomials over nite elds of large characteristic, and a regularity lemma for de nable sets. http://arxiv.org/pdf/1211.2894v4.pdf

[4] Wikipedia. Szemeredi regularity lemma. https://en.wikipedia.org/wiki/Szemer%C3%A9di_regularity_lemma

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