报告人：Lechao Xiao，宾夕法尼亚大学

摘要：One basic problem in algebra is finding roots for a polynomial. A central topic in modern harmonic analysis is finding (sharp) estimates for various oscillatory integrals. In the 17th century, Newton introduced a method, known as Newton-Puiseux algorithm, for solving a polynomial $f(x,y) = 0$ by a fractional power series, $y = y(x^{/frac 1 m})$. In this talk, we will illustrate how one can upgrade this algorithm to find sharp estimates for some oscillatory integrals.