报告简介：
    Hilbert’s Tenth Problem (HTP) asks for an effective algorithm to test whether an arbitrary polynomial equation P(x1; : : : ; xn) = 0 (with integer coefficients) has solutions over the ring of integers. This was finally solved by Matiyasevich in 1970 negatively.In this talk we review the historical developments towards the solution of HTP as well as some related tools including coding ideas and Lucas sequences. We will also introduce some further results after the solution of HTP; for example, the speaker has shown that there is no algorithm to decide whether an arbitrary polynomial equation P(x1; : : : ; x11) = 0 (with integer coefficients and 11 unknowns) has integral solutions or not.

报告人简介：
    孙智伟，1965年10月生。现为南京大学数学系教授、博士生导师，数学系数学与应用数学专业主任, 其研究方向为组合数论。他获过多项荣誉与奖励，例如：教育部首届青年教师奖（2000）,国家杰出青年科学基金（2005-2008）与国务院政府特殊津贴(2011)。他是《Journal of Combinatorics and Number Theory（组合与数论杂志）》的创刊主编(2009年至今), 《中国数学会通讯》现任编委（2016-）。曾多次应邀去美国、欧洲、香港、台湾等地访问讲学或担任客座教授。他在数论与组合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.（美国数学会汇刊）》等SCI杂志上发表了一百多篇学术论文。其工作被一些著名数学家（如Fields奖获得者T. Tao与著名组合学家N. Alon）在专著或论文中引用。他还提出了许多原创性数学猜想，引起国际同行的关注与研究。