Thesis links

Families and dichotomies in the circle method, Ph.D. Thesis, Princeton University, 2022. URL: http://arks.princeton.edu/ark:/88435/dsp01rf55zb86g (in Princeton's DataSpace). An unofficial single-spaced version (131 pages), differing mostly in the page numbering, can be found here (with main source here and full source here).

Note: Papers I, II, III below can be read independently. See here for some short descriptions of I, II, III and other related work.

Links to individual papers and drafts

(The following are roughly listed in reverse chronological order, at least morally.)

Paper III: Sums of cubes and the Ratios Conjectures
Version of April 19, 2023: arXiv:2108.03398v2 (61 pages)
Paper II: Special cubic zeros and the dual variety
J. Lond. Math. Soc. (2) 110 (2024), no. 3, Paper No. e12975, 35pp
(*) Restricted moments of cubic Weyl sums
Version of August 7, 2021 (rough draft): PDF (15 pages); source files
Paper I: Diagonal cubic forms and the large sieve
Version of April 18, 2023: arXiv:2108.03395v2 (23 pages)
(*) Axiomatizing Bombieri–Huxley
Version of August 7, 2021 (rough draft): PDF (14 pages); source files
(*) When does density beat Hua?
Version of August 7, 2021 (rough draft): PDF (18 pages); source files

Note: The works labeled with a star (*) are supplements to Paper I.