欢迎进入深圳大学数学与统计学院!

您当前所在位置: 首页 > 科学研究 > 学术交流 > 正文
学术交流

学术报告四:Hilbert's Tenth Problem for diophantine equations over Z[i] with few unknowns

来源:

作者:

时间:2021-01-13 14:37 

数学与统计学院学术报告[2021] 004

(高水平大学建设系列报告504)

报告题目: Hilbert's Tenth Problem for diophantine equations over Z[i] with few unknowns

报告人:孙智伟教授  (南京大学

报告时间:2021114930-1030

报告地点:汇星楼(科技楼)514   

报告内容:Hilbert’s Tenth Problem (HTP) asked for an algorithm to determine whether an arbitrary polynomial equation with integer coefficients has solutions over the ring of integers. This was finally solved negatively by Yu. Matiyasevich in 1970. HTP over the Gaussian ring Z[i] was proved to be unsolvable by J. Denef in 1975.

In this talk we introduce the recent work of Matiyasevich and the speaker. We prove that there is no algorithm to decide whether an arbitrarily given polynomial equation P(z1, . . . , z52) = 0 (with integer coefficients) over Z[i] is solvable or not.

报告人简历:孙智伟,南京大学数学系教授、博士生导师,其研究方向为组合数论与加法组合。他获过多项荣誉与奖励,例如:教育部首届青年教师奖、国家杰出青年科学基金与国务院政府特殊津贴。他是《Journal of Combinatorics and Number Theory》的创刊主编,《中国数学会通讯》与SCI期刊《Electronic Research Archive》现任编委。他在组合与数论交叉领域有许多创新成果, 迄今已在国外著名数学期刊《Trans. Amer. Math. Soc.》等SCI杂志上发表了一百多篇学术论文。他还提出了许多原创性数学猜想,引起一些国际著名数学家(如Fields奖获得者J. Bourgain)的关注与研究。

欢迎感兴趣的师生参加!

                          数学与统计学院

 

                                                20210113

地址:中国广东深圳大学科技楼四层

邮编:518060

电话:0755-26534791