Number Theory • Mathematics • University of Warwick

Office B2.19 • Zeeman Building • Coventry CV4 7AL • simon.rydin-myerson [at] warwick.ac.uk • he/him/his or they/them/theirs • Please call me Simon

I study the solutions to equations and inequalities in whole numbers. These are called Diophantine problems and they’re part of number theory. I use “analytic” arguments which are often fairly elementary, which makes it analytic number theory.

I’ve become interested in something which seems very different: nonlinear dispersive partial differential equations (nonlinear dispersive PDEs). This is a type of mathematical model which describes physical systems from ocean waves to fibre optic cables.

Systems of forms in many variables. (arXiv:1709.08917, improved version in preparation, see my HCM lectures for details, slides)

A two dimensional version of the delta symbol method, with Li, J.; and Vishe, P. (in preparation, slides)

A question about points on an elliptic curve with prime denominator. (arXiv:2307.09406, 2023, edited version of an open question to the problem session of JA2023, communicated there by Michel Waldschmidt)

Additive problems with almost prime squares, with Blomer, V.; Grimmelt, L.; and Li, J., Geom. Funct. Anal. (doi:10.1007/s00039-023-00635-w, 2023, slides)

The elliptic sieve and Brauer groups, with Bhakta, S.; Loughran, D.; and Nakahara, M., Proc. London Math. Soc., 126:1884-1922 (doi:10.1112/plms.12520, 2023, video version, slides)

Bounds for spectral projectors on generic tori, with Germain, P., Math. Annalen (doi:10.1007/s00208-022-02547-w, 2022, slides)

Bounds for spectral projectors on the Euclidean cylinder, with Germain, P., Comptes Rendus Math., 360:1257-1262 (doi:10.5802/crmath.378, 2022)

Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori, with Deng, Y.; Germain, P.; and Guth, L., Amer. J. Math., 144(3)701-745 (doi:10.1353/ajm.2022.0014, 2022, fulltext)

Bounds for spectral projectors on tori, with Germain, P., Forum Math. Sigma, 10:e24 (doi:10.1017/fms.2022.18, 2022)

Systems of cubic forms in many variables. J. Reine Agnew. Math. (Crelles Journal), 2019(757)309-328 (doi:10.1515/crelle-2017-0040, 2019)

Quadratic forms and systems of forms in many variables. Invent. math., 213:205-235 (doi:10.1007/s00222-018-0789-x, 2018)

Systems of many forms. DPhil thesis, University of Oxford (uuid:a9932e90-4784-466a-a694-d387c1228533, 2016)

Real and rational systems of forms. Oberwolfach Rep., 13(4)3013-3014 (doi:10.4171/OWR/2016/53, 2016, fulltext)

- I wrote some slides about the circle method for forms in rather few variables, in the style of Tran and Wang; this was for the London Number Theory Seminar analytic study group.
- I am one of Nuno Arala Santos' PhD supervisors.
- These are the 4th year projects I can offer; I also offer URSS projects along similar lines.

**CV**: https://www.dropbox.com/s/0fbpufvc9mkew73/cv.pdf?raw=1**Funding**: https://warwick.ac.uk/research/supporting-talent/fellowships/sci-fellowships/ecr/simon-myerson**Work**: https://warwick.ac.uk/fac/sci/maths/people/staff/myerson**Name**: https://www.name-coach.com/simon-rydinmyerson**arXiv**: https://arxiv.org/a/myerson_s_1**Publications**: https://wrap.warwick.ac.uk/view/author_id/381400.html**Phone**: https://peoplesearch.warwick.ac.uk/profile/1972891**ORCID**: https://orcid.org/0000-0002-1486-6054