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 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 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 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]