2033 Sheridan Rd, Evanston, IL 60208, USA

*Large subsets of discrete hypersurfaces in $\mathbb{Z}^d$ contain arbitrarily many collinear points*(with Joel Moreira),

European Journal of Combinatorics, Volume 54, 2016, pp. 163-176.

(doi, arXiv)*Revisiting the Nilpotent Polynomial Hales-Jewett Theorem*(with John H. Johnson),

Advances in Mathematics, Volume 321, 2017, pp. 269-286.

(doi, arXiv)*On the density of coprime tuples of the form $(n,\lfloor f_1(n)\rfloor,\ldots,\lfloor f_k(n)\rfloor)$, where $f_1,\ldots,f_k$ are functions from a Hardy field*(with Vitaly Bergelson),

Number Theory - Diophantine Problems, Uniform Distribution and Applications, Festschrift in Honour of Robert F. Tichy's 60th Birthday (C. Elsholtz and P. Grabner, eds.), Springer International Publishing, Cham, 2017, pp. 109-135.

(doi, arXiv)*A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems*(with Joel Moreira),

to appear in Ergodic Theory and Dynamical Systems (published online September 2017).

(doi, arXiv)*Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics*(with with Vitaly Bergelson, Joanna Kułaga-Przymus and Mariusz Lemanczyk),

to appear in Ergodic Theory and Dynamical Systems.

(arXiv)*A generalization of Kátai’s orthogonality criterion with applications*(with with with Vitaly Bergelson, Joanna Kułaga-Przymus and Mariusz Lemanczyk),

to appear in Discrete & Continuous Dynamical Systems.

(arXiv)*A structure theorem for level sets of multiplicative functions and applications*(with with with with Vitaly Bergelson, Joanna Kułaga-Przymus and Mariusz Lemanczyk),

to appear in International Mathematics Research Notices.

(arXiv)*A proof of the Erdős sumset conjecture*(with Joel Moreira and Donald Robertson),

to appear in Annals of Mathematics.

(arXiv)*Disjointness for measurably distal group actions and applications*(with Joel Moreira and Donald Robertson),

submitted.

(arXiv)*Single and multiple recurrence along non-polynomial sequences*(with Vitaly Bergelson and Joel Moreira),

submitted.

(arXiv)*Multiplicative combinatorial properties of return time sets in minimal dynamical systems*(with Daniel Glasscock and Andreas Koutsogiannis),

submitted.

(arXiv)