(2022-12-17) Seminar: Daqing Wan--Computing Zeta Functions of Large Polynomial Systems over Finite Fields

发布者:杨璐发布时间:2022-12-12浏览次数:151

万大庆  教授学术报告


Title: Computing Zeta Functions of Large Polynomial Systems over Finite Fields

Speaker: Prof. Daqing Wan(万大庆)

Affiliation: University of California at Irvine (加州大学尔湾分校)

Time: 10:00-11:00, Sat, Dec 17th, 2022 (UTC+8, Beijing Time)

Venue腾讯会议/VooV Meeting825-517-160

     入会链接https://meeting.tencent.com/dm/zZFtaqjhMwOu

Inviter:Hao Zhang(张浩),Xia Wu(吴霞)



Abstract
Efficient computation of the zeta function is of fundamental 
importance in algorithmic arithmetic geometry. In the general case, the only known non-trivial algorithms are the p-adic algorithms of Lauder-Wan (2008) and Harvey (2015). Both algorithms are exponential in the number of the defining equations. In this introductory talk, we explain an improved algorithm which is polynomial in terms of the number of defining equations. The key is an effective version of the classical Kronecker theorem for finite fields of suitably large size. This is based on joint work with Qi Cheng and Maurice Rojas (Journal of Complexity, 2022).


Speaker

万大庆,美国加州大学尔湾分校教授其于1991博士毕业于华盛顿大学,导师为数论名家N. Koblitz教授。后在内华达大学和宾夕法尼亚州立大学任教六年,于1997年到美国加州大学尔湾分校担任副教授,2001年起任教授。万教授被评为教育部海外杰出青年,曾入选中科院百人计划,获得世界华人数学家大会晨兴数学银奖。

万教授的研究方向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,解决了现代数论中的若干著名猜想,包括Dwork猜想,Katz猜想,Gouvea–Mazur猜想,Adolphson-Sperber猜想等,已在数学顶尖杂志《Annals of Mathematic》,《Invent. Math.》,《J. Amer. Math. Soc.》上发表多篇文章,其研究工作在算术代数几何的许多重要领域产生重要影响。近年来,万教授在计算数论、编码和计算复杂性领域也做出了杰出的工作,其结果发表在FOCSSTOCFOCMIEEE IT等计算机和信息理论的顶级杂志上。现为国际著名数学杂志《Journal of Number Theory》和《Finite Fields and Their Applications》的编委。


0