Counting solutions of polynomial systems over finite fields

主讲人:万大庆 教授(美国加州大学欧文分校University of California, Irvine)
时间:2020年9月9日上午10:00-11:00   地点:腾讯会议ID:260 140 265 会议密码:314159

学术海报

【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