Papers and Preprints
On Rado conditions for nonlinear Diophantine equations, (joint with Jordan M. Barrett and Martino
Lupini). Preprint available at [arXiv].
Optimal lower bounds for multiple recurrence, (joint work with Sebastian Donoso, Anh Ngoc Le and Wenbo Sun). To appear in Ergodic Theory Dynam. Systems, preprint available at [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). Submitted, preprint available at [arXiv][blog post]
Disjointness for measurably distal group actions and applications, (joint work with Florian K. Richter and Donald Robertson). Submitted, preprint available at [arXiv]
A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems, (joint work with Florian K. Richter). To appear in Ergodic Theory Dynam. Systems, preprint available at [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), Jornal 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]