Papers

1. Corners with polynomial side length, with N. Kravitz and J. Leng, arXiv:2407.08637, arxiv, slides.

2. Quantitative concatenation for polynomial box norms, with N. Kravitz and J. Leng,  arXiv:2407.08636, arxiv, slides.

3. Multidimensional polynomial patterns over finite fields: bounds, counting estimates and Gowers norm control, Adv. Math., 448:109700, 2024, journal, arxiv.

4. Degree lowering for ergodic averages along arithmetic progressions, with N. Frantzikinakis, arXiv:2212.09819, to appear in Journal d'Analyse Mathématique, arxiv, slides, video.

5. Seminorm control for ergodic averages with commuting transformations and pairwise dependent polynomial iterates, with N. Frantzikinakis, Ergodic Theory Dynam. Systems, 2023;43(12):4074-4137, journal, arxiv.

6. Joint ergodicity for commuting transformations and applications to polynomial sequences, with N. Frantzikinakis, arXiv:2207.12288, arxiv. slides, video, Nikos' video .

7. On a continuous Sárközy type problem, with T. Orponen and T. Sahlsten, Inter. Math. Res. Not. IMRN, 2022;, rnac168, journal, arxiv, slides.

8. Multidimensional polynomial Szemerédi theorem in finite fields for polynomials of distinct degrees, Israel J. Math. 259 (2024), 589-620, journal, arxiv.

9. On several notions of complexity of polynomial progressions, Ergodic Theory Dynam. Systems, 2023;43(4):1269-1323, journal, arxiv, slides (easy version), slides (advanced version), video.

10. True complexity of polynomial progressions in finite fields, Proc. Edinb. Math. Soc., 64.3 (2021), 448-500, journal, arxiv. 

11. Further bounds in the polynomial Szemerédi theorem in finite fields,  Acta Arith. 198 (2021), 77-108, journal, arxiv.

12. The unreasonable rigidity of Ulam sets, with J. Hinman, A. Schlesinger, and A. Sheydvasser, J. Number Theory 194 (2019), 409-425, journal, slides.

13. Rigidity of Ulam sets and sequences, with J. Hinman, A. Schlesinger, and A. Sheydvasser, Involve 12-3 (2019), 521-539, journal, slides.

14. Structures in additive sequences, Acta Arith. 186.3 (2018), 273-300, journal, arxiv.

There may be minor differences between the journal and arXiv versions of my articles. 

General talks:

• The Szemerédi theorem and beyond, slides.

• Recent developments in the polynomial Szemerédi theorem, slides.

• Analytic methods in the polynomial Szemerédi theorem, slides.

• A short introduction to additive combinatorics, slides, video.

• Many mysteries of the Ulam sequences, slides.