*Extending weakly polynomial functions from high rank varieties*, with David Kazhdan.

Preprint available at [arxiv]

*On ranks of polynomials*, with David Kazhdan.

Selecta Mathematica [arxiv] [journal]

*Polynomial functions as splines.*, with David Kazhdan.

Preprint available at [arxiv]

*Extending linear and quadratic functions from high rank varieties.*, with David Kazhdan.

Preprint available at [arxiv]

*Approximate Cohomology*, with David Kazhdan.

Selecta Mathematica [arxiv][journal]

*On the bias of cubic polynomials*, with David Kazhdan.

Selecta Mathematica [arxiv][journal]

*Polynomial patterns in the primes*, with Terence Tao.

Forum of Mathematics, Pi. [arxiv] [journal] [blog, video]

*Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors*, with Terence Tao.

Discrete Analysis. [arxiv] [journal] [blog, video]

*Narrow progressions in the primes*, with Terence Tao.

Special issue Analytic Number Theory in honor of the 60th birthday of Helmut Maier. [arxiv] [journal [blog][video]

*Linear equations in primes and dynamics of nilmanifolds*.

Proceedings of ICM 2014. [arxiv][video]

*A multi-dimensional Szemer\'edi theorem for the primes via a correspondence principle*, with Terence Tao.

Israel Journal of Mathematics. [arxiv][blog]

*Multiple recurrence and convergence results associated to F*, with Vitaly Bergelson, Terence Tao.

_{p}^{∞}-actionJournal d'Analyse Mathematique, Volume 127, Issue 1, 329-378, (2015) [arxiv][blog]

*Distjointness of Mobius from horocycle flows*, with Jean Bourgain and Peter Sarnak.

From Fourier Analysis and Number Theory to Radon Transforms and Geometry, Developments in Mathematics, Vol. 28. [journal] [arxiv][A note on Mobius orthogonality to nilsequences]

*The inverse conjecture for the Gowers norm over finite fields in low characteristic*, with Terence Tao.

Ann. Comb. 16 (2012), 121-188. [arxiv][journal][blog]

*An inverse theorem for the Gowers U*, with Ben Green, Terence Tao.

^{s+1}[N]-normAnnals of Math, Volume 176 (2012), Issue 2, 1231-1372. [arxiv][ journal][blog, video]

*The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems*, with Vitaly Bergelson, Alexander Leibman.

C. R. Math. Acad. Sci. Paris 349 (2011), no. 3-4, 123-125. [arxiv][journal]

*An inverse theorem for the Gowers U*, with Ben Green, Terence Tao.

^{s+1}[N]-normElectronic Research Announcements 18 (2011), 69 - 90. [arxiv][journal] [blog]

*Multiple recurrence and convergence along the primes*, with Trevor Wooley.

American Journal of Mathematics 134 (2012), no. 6, 1705-1732. [arxiv][journal][video]

*An inverse theorem for the Gowers U*, with Ben Green, Terence Tao.

^{4}-normGlasg. Math. J. 53 (2011), no. 1, 1-50. [arxiv][journal]

*An inverse theorem for the uniformity seminorms associated with the action of F*, with Vitaly Bergelson, Terence Tao.

_{p}^{∞}Geom. Funct. Anal. 19 (2010), No. 6, 1539-1596.[arxiv] [journal][blog, video]

*The inverse conjecture for the Gowers norm over finite fields via the correspondence principle*, with Terence Tao.

Analysis & PDE Vol. 3 (2010), No. 1, 1-20. [arxiv][journal][blog, video]

*The primes contain arbitrarily long polynomial progression*, with Terence Tao.

Acta Math. 201 (2008), no. 2, 213--305. [arxiv][journal][blog]

*Universal Characteristic Factors and Furstenberg Averages*.

J. Amer. Math. Soc. 20 (2007), 53-97. [arxiv][Journal][video]

*Nilfactors of R*

^{m}-actions and configurations in sets of positive upper density in R^{m}.J. Anal. Math. 99 (2006), 249-266. [arxiv][Journal]

*A non-conventional ergodic theorem for a nilsystem*.

Ergodic Theory and Dynamical Systems 25 (2005) no. 4 1357-1370. [arxiv][Journal]

*Non-conventional ergodic averages*.

PhD Thesis. [pdf]

*An application of ergodic theory to a problem in geometric Ramsey theory*.

Israel Journal of Math. 114 (1999) 271-288. [Journal]

#### Presentations:

Gauss arithmetic geometric mean (agm)EMS Lecture Series: I II