# Papers and Preprints

Monochromatic sums and products in $\mathbb{N}$, submitted. [arXiv]

Van der Corput’s difference theorem: some moders developments (joint work with Vitaly Bergelson), to appear in special issue of Indag. Math. dedicated to van der Corput. [arXiv]

Measure preserving actions of affine semigroups and $\{x+y,xy\}$ patterns (joint work with Vitaly Bergelson), to appear in Ergodic Theory Dynam. Systems. [arXiv][blog post]

Large subsets of discrete hypersurfaces in $\mathbb{Z}^d$ contain arbitrarily many collinear points (joint work with Florian K. Richter), submitted. [arXiv][blog post]

New polynomial and multidimensional extensions of classical partition results (joint work with Vitaly Bergelson and John H. Johnson), submitted. [arXiv][blog post]

A conditional construction of restricted isometries (joint work with Afonso S. Bandeira and Dustin G. Mixon), to appear in International Mathematical Research Notices. [arXiv][blog post]

Derandomizing restricted isometries via the Legendre symbol (joint work with Afonso S. Bandeira, Matthew Fickus and Dustin G. Mixon), to appear in Constr. Approx.. [arXiv][blog post]

Ergodic theorem involving additive and multiplicative groups of a field and $\{x+y,xy\}$ patterns (joint work with Vitaly Bergelson), to appear in Ergodic Theory Dynam. Systems. [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]