【摘要】A fundamental algorithmic problem in mathematics and computer science is to efficiently count the solutions of a multivariate polynomial system over a finite field, and over all of its finite extensions. All general algorithms so far are fully exponential in terms of the number of equations. In a recent joint work with Q. Cheng and M. Rojas, we have reduced this exponential dependence to a polynomial dependence on the number of equations. A key new ingredient is an effective version of the classical Kronecker theorem which says that set-theoretically any polynomial system in n variables can be defined by n+1 equations if the field is not too small. This will be an introductory lecture toward a general audience.

【报告人简介】万大庆现为美国加州大学欧文分校（University of California, Irvine）教授。中科院数学院数学研究所海外杰出访问教授，清华大学高研中心海外访问教授，教育部海外杰出青年，获得国际华人数学家大会晨兴（Morningside）数学银奖。

现为国际著名数学杂志《Journal of Number Theory》、《Finite Fields and Their Applications》编委，在数论、算术几何、编码、密码和计算复杂性领域都有很高的研究成就。他的研究兴趣是数论和算术代数几何，尤其是有限域上的zeta函数和L-函数。解决了一系列现代数论中的若干著名猜想，包括Dwork 猜想，Katz猜想，Gouvea–Mazur猜想等，已在数学顶尖杂志Annals of Mathematic、Inventiones Mathematicae、Journal of American Mathematical Society等发表了多篇文章。 在计算数论、编码和计算复杂性等领域的多项工作发表在FOCS、STOC、FOCM等计算机科学领域著名会议论文上。

会议直播: https://meeting.tencent.com/l/xkz0ElWv2NfT