Papers and Preprints
A structure theorem for polynomial return-time sets in minimal systems (with Daniel Glasscock, Andreas Koutsogiannis, Anh N. Le, Florian K. Richter and Donald Robertson). Submitted.
Metric uniform distribution on analytic curves (with Vitaly Bergelson). Submitted.
The Density Finite Sums Theorem (with Bryna Kra, Florian K. Richter and Donald Robertson). Invent. math. 243, 1–31 (2026).
Partition regularity of generalized Pythagorean pairs (with Nikos Frantzikinakis and Oleksiy Klurman). Submitted.
Interpolation sets for dynamical systems (with Andreas Koutsogiannis, Anh N. Le, Ronnie Pavlov and Florian K. Richter). Trans. Amer. Math. Soc. 378 (2025), no. 2, 1373–1400
Problems on infinite sumset configurations in the integers and beyond (with Bryna Kra, Florian K. Richter and Donald Robertson). Bull. Amer. Math. Soc. 62 (2025), 537–574.
Partition regularity of Pythagorean pairs (with Nikos Frantzikinakis and Oleksiy Klurman). Forum Math. Pi 13 (2025) Paper No. e5, 52 pp.
Averages of completely multiplicative functions over the Gaussian integers – a dynamical approach (with Sebastian Donoso, Anh Ngoc Le and Wenbo Sun). Trans. Amer. Math. Soc. 377 (2024), no. 10, 7081–7115.
A proof of Erd艖s鈥檚 B + B + t conjecture (with Bryna Kra, Florian K. Richter and Donald Robertson). Commun. Amer. Math. Soc. 4 (2024), 480–494.
Infinite Sumsets in Sets with Positive Density (with Bryna Kra, Florian K. Richter and Donald Robertson). J. Amer. Math. Soc. 37 (2024), no. 3, 637–682.
A combinatorial proof of a sumset conjecture of Furstenberg (with Daniel Glasscock and Florian K. Richter). Combinatorica 43 (2023), no. 2, 299–328.
Additive averages of multiplicative correlation sequences and applications (with Sebastian Donoso, Anh Ngoc Le and Wenbo Sun). J. Anal. Math. 149 (2023), no. 2, 719–761.
Additive and Geometric transversality of fractal sets in the integers, (with Daniel Glasscock and Florian K. Richter). J. London Math. Soc. (2) 109 (2024), no 5, Paper No. e12902, 55 pp.
Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications (with Vitaly Bergelson and Florian K. Richter). Advances in Mathematics 443 (2024) Paper No. 109597, 50 pp.
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.
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.
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.
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.
A proof of a sumset conjecture of Erd艖s, (joint work with Florian K. Richter and Donald Robertson).
Annals of Mathematics, (2) 189 (2019), no. 2, 605–652.
Single and multiple recurrence along non-polynomial sequences, (joint work with Vitaly Bergelson and Florian K. Richter). Advances in Mathematics 368 (2020), 107–146.
Disjointness for measurably distal group actions and applications, (joint work with Florian K. Richter and Donald Robertson). Ergodic Theory Dynam. Systems 43 (2023), no. 6, 1952–1979.
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.
Monochromatic sums and products in $\mathbb{N}$, Annals of Mathematics (2) 185 (2017), no. 3, 1069–1090.
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).
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), Journal of Combinatorial Theory, Series A 147 (2017), 119–154.
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.
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.
Ergodic theorem involving additive and multiplicative groups of a field and
Usando probabilidades para aproximar fun莽玫es por polin贸mios (in portuguese), N煤meros, Cirurgias e N贸s de Gravata: 10 anos de Semin谩rio Diagonal no IST. [pdf]
Phd thesis
(2016). [pdf]
Other
Ergodic Ramsey Theory notes (there is some overlap with the previous notes)