I'm interested in properties of polynomials of fixed degree in arbitrarily many variables. This setting has proved a fruitful one in such diverse areas as higher order Fourier analysis, the Hardy-Littlewood circle method and Stillman's conjecture. Strength, also known as Schmidt rank or partition rank, plays a central role.
Preprints
Two improvements in Birch’s theorem on forms. arXiv.
Slice rank and analytic rank for trilinear forms. arXiv.
Small ideals in polynomial rings and applications. arXiv.
Published
Schmidt rank and singularities (with D. Kazhdan and A. Polishchuk). Ukrainian Mathematical Journal. arXiv Journal
On rank in algebraic closure (with T. Ziegler). Selecta Mathematica. arXiv Journal
Relative rank and regularization. (with T. Ziegler) Forum of Mathematics, Sigma. arXiv Journal
Bias implies low rank for quartic polynomials. arXiv. M.Sc. thesis.
On maximizing the speed of a random walk in fixed environments (with A. Shapira). Electronic Communications in Probability. arXiv Journal