关于举行沙敏博士学术报告的通知
报告题目:Some properties of integer polynomials and their applications in linear recurrence sequences
报 告 人:沙敏 博士(澳大利亚的新南威尔士大学数学系)
报告时间: 2015年3月6日下午3:00--4:00
报告地点:4号楼 4318室
欢迎广大师生参加。
数学学院
2015年2月27日
附:
报告人简介:沙敏博士2007年7月毕业于华南理工大学(数学与应用数学专业),当年保送到清华大学攻读基础数学硕士学位并于2010年7月毕业(获得学校优秀研究生称号),随后公派到法国的波尔多大学攻读基础数学博士学位并于2013年9月毕业。目前在澳大利亚的新南威尔士大学数学系做博士后。研究兴趣主要是经典数论、丢番图几何、算术动力系统、椭圆曲线的算术及其应用、以及函数域上的线性递归序列。在Journal of Combinatorial Theory Series B、International Mathematics Research Notices、Experimental Mathematics、Proceedings of the American Mathematical Society、Monatshefte fur Mathematik等国外数学刊物上发表论文14篇,在审论文6篇。从2012年开始担任美国《数学评论》评论员,是SIAM Journal on Discrete Mathematics、Finite Fields and Their Applications等多个数学杂志的审稿人。
报告摘要: A real polynomial is called degenerate if it has two distinct roots whose quotient is a root of unity, and it is called dominant if it has exactly one root with largest modulus among all its roots. We first show that almost all integer polynomials are non-degenerate, and almost all monic integer polynomials are dominant. It is also proved that almost all integer polynomials have exactly one root or two roots with largest modulus. The applications of these results suggest that almost every randomly generated linear recurrence sequence (LRS) is exactly what we usually prefer it to be, and the Skolem problem of LRS is done for almost all LRS of algebraic numbers with integer coefficients (or rational coefficients). Note that the Skolem problem is widely open in general case.