How many values a polynomial misses?

报告题目How many values a polynomial misses?


报告人Daqing Wan万大庆 (University of California, Irvine, USA)






摘要: A polynomial f(x) over a field F induces a map from the field F to itself. If the polynomial map f misses one value, then it is expected that the polynomial map would miss many values. This is still a wide open problem in general. In this expository talk, we will introduce various results and open problems in this direction, and discuss its connections to different branches of mathematics, particularly number theory, and finite group theory.


报告人简介:万大庆,美国加州大学欧文分校(University of California, Irvine)教授。中科院数学院研究所海外杰出访问教授,365体育官网app下载高研中心海外访问教授,教育部海外杰出青年,曾入选中科院百人计划,获得国际华人数学家晨兴(Morningside)数学银奖。现为国际著名数论杂志《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 MathematicInventiones MathematicaeJournal of American Mathematical Society等发表了多篇文章。 目前在计算数论、编码和计算复杂性领域有多项工作,这些结果分别发表在FOCSSTOCFOCM等著名计算机杂志上。近些年,他利用数论去研究算法,编码理论和计算机科学,成效不凡。




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