Sean Prendiville
Lancaster University
s.prendiville@lancaster.ac.uk
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.
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).