Graduate Programs      Graduate Home Ph D Programs Masters Degree Ph D Program Requirements Course Descriptions Current Courses Admissions Current Graduate Students Graduate Student Seminar SIAM Chapter Seminar Recent Graduates Incoming Students Graduate Seminar Zilin Jiang Carnegie Mellon University Title: Hardy--Littlewood Circle Method and Waring's Problem Abstract: Let $A$ be a subset of the natural numbers, and set $r(n; s, A) :=$ number of ways to write $n$ as a sum of $s$ elements of $A$. Many important problems can be phrased in terms of these functions. For example, let $A$ be the set of prime numbers. Then Goldbach conjecture is equivalent to $r(n; 2, A) > 0$ for all $n$ even and greater than $2$. The Waring's problem asks for the asymptotics for $r(n; s, A)$, where $A$ is the set of $k$th powers. In this talk, I will try to sketch out some of the major ideas in the Hardy--Littlewood Circle Method in the context of Waring's ProblemDate: Thursday, April 9, 2015Time: 5:30 pmLocation: Wean Hall 8220Submitted by:  Zilin Jiang