Papers and Preprints
Partition regularity of generalized Pythagorean pairs (with Nikos Frantzikinakis and Oleksiy Klurman). Submitted. [arXiv][blog post]
Interpolation sets for dynamical systems (with Andreas Koutsogiannis, Anh N. Le, Ronnie Pavlov and Florian K. Richter). Submitted. [arXiv]
Problems on infinite sumset configurations in the integers and beyond (with Bryna Kra, Florian K. Richter and Donald Robertson). Submitted. [arXiv]
Partition regularity of Pythagorean pairs (with Nikos Frantzikinakis and Oleksiy Klurman). Submitted. [arXiv][blog post]
Averages of completely multiplicative functions over the Gaussian integers – a dynamical approach (with Sebastian Donoso, Anh Ngoc Le and Wenbo Sun). Submitted. [arXiv]
A proof of Erdős’s B + B + t conjecture (with Bryna Kra, Florian K. Richter and Donald Robertson). Commun. Amer. Math. Soc. 4 (2024), 480–494. [arXiv] [blog post]
Infinite Sumsets in Sets with Positive Density (with Bryna Kra, Florian K. Richter and Donald Robertson). J. Amer. Math. Soc. 37 (2024), no. 3, 637–682. [DOI] [arXiv] [blog post]
A combinatorial proof of a sumset conjecture of Furstenberg (with Daniel Glasscock and Florian K. Richter). Combinatorica 43 (2023), no. 2, 299–328. [arXiv].
Additive averages of multiplicative correlation sequences and applications (with Sebastian Donoso, Anh Ngoc Le and Wenbo Sun). J. Anal. Math. 149 (2023), no. 2, 719–761. [arXiv].
Additive and Geometric transversality of fractal sets in the integers, (with Daniel Glasscock and Florian K. Richter). J. London Math. Soc. (2) 109 (2024), no 5, Paper No. e12902, 55 pp. [arXiv] [blog post]
Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications (with Vitaly Bergelson and Florian K. Richter). Advances in Mathematics 443 (2024) Paper No. 109597, 50 pp. [arXiv] [blog post].
Structure of multicorrelation sequences with integer part polynomial iterates along primes, (joint with Andreas Koutsogiannis, Anh Ngoc Le and Florian Richter). Proc. Amer. Math. Soc. 149 (2021), no. 1, 209–216. [arXiv] [blog post]
A decomposition of multicorrelation sequences for commuting transformations along primes,
(joint with Anh N. Le and Florian K. Richter). Discrete Anal. (2021), no. 4, 27 pp. [arXiv].
On Rado conditions for nonlinear Diophantine equations, (joint with Jordan M. Barrett and Martino Lupini). European J. Combin. 94 (2021), Paper no. 103277, 20 pp. [arXiv].
Optimal lower bounds for multiple recurrence, (joint work with Sebastian Donoso, Anh Ngoc Le and Wenbo Sun). Ergodic Theory Dynam. Systems 41 (2021), no. 2, 379–407. [arXiv]
A proof of a sumset conjecture of Erdős, (joint work with Florian K. Richter and Donald Robertson).
Annals of Mathematics, (2) 189 (2019), no. 2, 605–652. [arXiv] [blog post]
Single and multiple recurrence along non-polynomial sequences, (joint work with Vitaly Bergelson and Florian K. Richter). Advances in Mathematics 368 (2020), 107–146. [arXiv] [blog post]
Disjointness for measurably distal group actions and applications, (joint work with Florian K. Richter and Donald Robertson). Ergodic Theory Dynam. Systems 43 (2023), no. 6, 1952–1979. [arXiv]
A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems, (joint work with Florian K. Richter). Ergodic Theory Dynam. Systems 39 (2019), no. 4, 1042–1070. [arXiv]
Monochromatic sums and products in $\mathbb{N}$, Annals of Mathematics (2) 185 (2017), no. 3, 1069–1090. [arXiv]
Van der Corput's difference theorem: some modern developments (joint work with Vitaly Bergelson), Indag. Math. (N.S.) 27 (2016), no. 2, 437–479 (special issue dedicated to van der Corput). [arXiv]
Measure preserving actions of affine semigroups and 
Large subsets of discrete hypersurfaces in 
New polynomial and multidimensional extensions of classical partition results (joint work with Vitaly Bergelson and John H. Johnson), Journal of Combinatorial Theory, Series A 147 (2017), 119–154. [arXiv] [blog post]
A conditional construction of restricted isometries (joint work with Afonso S. Bandeira and Dustin G. Mixon), International Mathematical Research Notices 2017, no. 2, 372–381. [arXiv] [blog post]
Derandomizing restricted isometries via the Legendre symbol (joint work with Afonso S. Bandeira, Matthew Fickus and Dustin G. Mixon), Constr. Approx. 43 (2016), no. 3, 409–424. [arXiv] [blog post]
Ergodic theorem involving additive and multiplicative groups of a field and
Usando probabilidades para aproximar funções por polinómios (in portuguese), Números, Cirurgias e Nós de Gravata: 10 anos de Seminário Diagonal no IST. [pdf]
Phd thesis
Partition regular polynomial patterns in commutative semigroups (2016). [pdf]
Other
Ergodic Ramsey Theory notes (there is some overlap with the previous notes)