Sean Prendiville

Lecture notes on Nonlinear Fourier analysis in additive combinatorics.

CV

s.prendiville@lancaster.ac.uk

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Research interests:  Additive combinatorics, analytic number theory, Fourier analysis

I am on the editorial board of Proceedings of the Royal Society of Edinburgh Section A: Mathematics.

We welcome excellent submissions in combinatorics and number theory, amongst many other areas.

I co-organise the Webinar in Additive Combinatorics.

Fourier methods in combinatorial number theory:

• Videos

• Lecture notes

Lecture notes on Fourier analysis in Ramsey theory.

Videos from the conference Arithmetic Ramsey Theory.

Research

• Extremal Sidon sets are Fourier uniform, with applications to partition regularity, with M. Ortega, J. Théor. Nombres Bordeaux (accepted). Video lecture. 

• Counting monochromatic solutions to diagonal Diophantine equations, Discrete Analysis (accepted). Video lecture.

• Solving equations in dense Sidon sets, Math. Proc. Cambridge. Phil. Soc. (accepted).

• A polylogarithmic bound in the nonlinear Roth theorem, with S. Peluse, International Mathematics Research Notices (to appear).

• The inverse theorem for the nonlinear Roth configuration: an exposition (expository).

• On the Ramsey number of the Brauer configuration, with J. Chapman, Bulletin of the London Mathematical Society (2020).

• Quantitative bounds in the nonlinear Roth theorem, with S. Peluse (submitted). Video lecture by Sarah Peluse. See also this blogpost of Terry Tao.

• Rado's criterion over squares and higher powers, with S. Chow and S. Lindqvist, Journal of the European Mathematical Society (to appear).  Video lectures: me,  Sofia Lindqvist.

• A transference approach to a Roth-type theorem in the squares, with T.D. Browning, International Mathematics Research Notices (2017).  Video lecture.

• Four variants of the Fourier-analytic transference principle, Online Journal of Analytic Combinatorics (2017).

• Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case, Discrete Analysis (2017).

• Improvements in Birch's theorem on forms in many variables, with T.D. Browning, Journal reine angew. Math. (2017).  Video lecture.

• Matrix progressions in multidimensional sets of integers, Mathematika (2015).

• Near-optimal mean value estimates for multidimensional Weyl sums, with S.T. Parsell and T.D. Wooley, Geometric and Functional Analysis (2013).

• Solution-free sets for sums of binary forms, Proceedings of the London Mathematical Society (2013). 

I contributed to this article in Quanta magazine on spectacular work of Sarah Peluse.

What I'm listening to: