报告题目：The distance to square-free polynomials

报告人: 沙敏

摘  要： Given an integer polynomial f, let L(f) be the sum of the absolute values of the coefficients of f. In 1960s, Turán asked whether there exists an absolute constant C such that for any integer polynomial f of degree d,  there is an irreducible integer polynomial g of degree at most d satisfying L(f-g) < C. Turán's problem remains open, although a number of partial results have been obtained.

In this talk, I will present some recent work on a variant of Turán's problem. For example, we prove that for any integer polynomial f, there exist infinitely many square-free integer polynomials g such that L(f-g) < 3. On the other hand, we show that this inequality cannot be replaced by L(f-g) < 2. (This is joint work with Artūras Dubickas)

报告时间：2018年5月31日（星期四）10:00-11:00

报告地点：威廉希尔中文网站三楼专家接待室

报告人简介：沙敏博士2007年本科毕业于华南理工大学，2010年和2013年在清华大学和法国的波尔多大学分别取得基础数学的硕士学位和博士学位。之后，先是在澳大利亚的新南威尔士大学做博士后，目前在澳大利亚的麦考瑞大学做校级博士后。研究兴趣主要是代数数论、算术动力系统、椭圆曲线的算术及其应用、有限域理论、数论里的图论问题、以及线性递归序列。在Transactions of the American Mathematical Society、Moscow Mathematical Journal、International Mathematics Research Notices、Journalof Combinatorial Theory Series B、Mathematische Zeitschrift等国外数学刊物上发表论文30余篇。从2012年开始担任美国《数学评论》评论员，是SIAM Journal on Discrete Mathematics、Proceedingsof the American Mathematical Society、Finite Fields and Their Applications等多个数学杂志的审稿人。