Dynamical Systems Seminar

I will discuss joint work with Vinay Kumaraswamy towards a conjecture of Wooley. Given a cubic polynomial in \(n\) variables with integer coefficients, a classical question asks how many zeros does the polynomial have in a box of bounded sidelength. Wooley predicted an asymptotic lower bound for this quantity which we establish once the number of variables \(n\) is large enough. The main tool is the Hardy-Littlewood circle method (with which I will assume no familiarity).