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Papers and Preprints

A combinatorial proof of a sumset conjecture of Furstenberg (with Daniel Glasscock and Florian K. Richter). Submitted. [arXiv].

Additive averages of multiplicative correlation sequences and applications (with Sebastian
Donoso, Anh Ngoc Le and Wenbo Sun). Submitted. [arXiv].

Additive transversality of fractal sets in the reals and the integers, (with Daniel Glasscock and
Florian K. Richter). Submitted. [arXiv][blog post]

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence
and combinatorial applications
(with Vitaly Bergelson and Florian K. Richter). Submitted. [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). Submitted. [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 \{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), 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 \{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