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 $\{x+y,xy\}$ patterns (joint work with Vitaly Bergelson), Ergodic Theory Dynam. Systems 38 (2018), no. 2, 473--498. [arXiv][blog post]

Large subsets of discrete hypersurfaces in $\mathbb{Z}^d$ contain arbitrarily many collinear points (joint work with Florian K. Richter), European J. Combin. 54 (2016), 163--176. [arXiv][blog post]

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 $\{x+y,xy\}$ patterns (joint work with Vitaly Bergelson), Ergodic Theory Dynam. Systems 37 (2017), no. 3, 673--692. [arXiv][blog post]

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 Theory notes