Analysis and Probability Seminar

Abstract: This is joint work with J. Wright, about bounds for oscillatory integrals and complete exponential sums with polynomial phases. Because of their appearance in various fields of mathematics (notably, in PDEs and number theory), a variety of techniques have been developed for bounding these objects. In this talk, I will present a unified approach that works over an arbitrary local field. A novel aspect emerges from our work: oscillatory integrals with "special phases" enjoy improved decay estimates when the frequency parameter goes to infinity.