I'm interested in properties of polynomials of fixed degree in many variables. This setting has proved fruitful for such diverse questions as the distribution of polynomials over finite fields, unirationality of hypersurfaces, counting integer zeros of polynomial equations and bounding the projective dimension of ideals in polynomial rings. Strength, also known as Schmidt rank or partition rank, plays a central role.
Density of solutions for systems of forms. Submitted.
Strength and partition rank under limits and field extensions (with A. Bik, J. Draisma and T. Ziegler). Submitted.
Strength is bounded linearly by Birch rank (with B. Baily). Submitted.
Two improvements in Birch’s theorem on forms (with A. Snowden). Submitted.
Slice rank and analytic rank for trilinear forms. Submitted.
Small ideals in polynomial rings and applications. Submitted.
Schmidt rank and singularities (with D. Kazhdan and A. Polishchuk). Ukrainian Mathematical Journal. arXiv
On rank in algebraic closure (with T. Ziegler). Selecta Mathematica. arXiv
Relative rank and regularization (with T. Ziegler). Forum of Mathematics, Sigma. arXiv
Bias implies low rank for quartic polynomials. M.Sc. thesis.
On maximizing the speed of a random walk in fixed environments (with A. Shapira). Electronic Communications in Probability. arXiv