Analysis Seminar: Semi-algebraic discrepancy estimates for skew-shift sequences
Speaker: Matthew Powell, Georgia Institute of Technology
Abstract: The discrepancy of a sequence essentially measures how often a sequence visits a particular set. We show that the semi-algebraic discrepancy of a skew-shift sequence on the b-dimensional torus \mathbb{T}^b behaves differently for large b and small b, with a transition at b = 6. The key to our analysis will be the Weyl summation method for exponential sums and the Vinogradov mean value theorem recently proved by Bourgain, Demeter, and Guth. If time permits, we will discuss applications to problems in mathematical physics. This is based on joint work with W. Liu and X. Wang of Texas A&M.
Host: Xiang Tang