Sean Prendiville

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.

During the pandemic, I co-organised the Webinar in Additive Combinatorics.

Lecture notes on Nonlinear Fourier analysis 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

• An inverse theorem for the Gowers U3-norm relative to quadratic level sets, (preprint).

• Quantitative bounds in the nonlinear Roth theorem, with Sarah Peluse, Inventiones Mathematicae (2024). Video lecture by Sarah Peluse. See also this blogpost of Terry Tao.

• Bounds in a popular multidimensional nonlinear Roth theorem, with Sarah Peluse and Xuancheng Shao, Journal of the LMS (2024).

• Extremal Sidon sets are Fourier uniform, with applications to partition regularity, with Miquel Ortega, J. Théor. Nombres Bordeaux (2023). Video lecture. 

• Counting monochromatic solutions to diagonal Diophantine equations, Discrete Analysis (2021). Video lecture.

• Solving equations in dense Sidon sets, Math. Proc. Cambridge. Phil. Soc. (2022).

• A polylogarithmic bound in the nonlinear Roth theorem, with Sarah Peluse, International Mathematics Research Notices (2022).

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

• Rado's criterion over squares and higher powers, with Sam Chow and Sofia Lindqvist, Journal of the European Mathematical Society (2021).  Video lectures: me,  Sofia Lindqvist.

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

• A transference approach to a Roth-type theorem in the squares, with Tim 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 Tim 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 Scott Parsell and Trevor 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: