应数学系和数学研究院张毅超教授邀请，西湖大学赵永强研究员将于6月15日至6月28日对6163银河线路检测中心数学系和数学研究院进行学术访问。访问期间将做系列报告，共计五到六次，具体时间如下：

报告1时间：2018年6月19日下午2：00-4：30

报告2时间：2018年6月20日下午2：00-4：30

报告3时间：2018年6月22日下午2：00-4：30

报告4时间：2018年6月24日下午2：00-4：30

报告5时间：2018年6月26日下午2：00-4：30

报告6时间：2018年6月27日下午2：00-4：30

    报告地点统一安排在诚意楼A102。报告主要内容是d-次型上的Artin猜想，具体内容见下面报告摘要。

报告摘要：It was conjectured by Artin that every degree-d form over the field of p-adic numbers with more than d^2 variables must have a nontrivial zero. Artin's conjecture is currently only known for linear, quadratic and cubic forms. The conjecture is known to be false in general. Counterexamples were first given by Terjanian and then by many others. However, all such known examples are of even degree and are, more or less, of the same particular type. There is much left to be discovered in this fascinating area of number theory. For example, it is still not known that whether Artin's conjecture holds for quintic forms. And, is there any counterexample to the conjecture with odd degree?

In this short course, we will give a friendly introduction to this conjecture, including results both in the positive direction and negative aspects. The various topics we plan to discuss are the following:

(1) Hensel's Lemma, Chevalley-Warning Theorems;

(2) Weil's conjecture for diagonal hypersurfaces;

(3) p-adic zeros of cubic forms in at least ten variables;

(4) Various counterexamples to Artin's conjecture by Terjanian, Browkin and, Lewis and Montgomery;

(5) Zeros of forms with many variables, Wooley's bound.

If time permits and the audiences have enough interests, we will also discuss Heath-Brown's recent results on quartic forms. We will try to make the course as self-contained as possible. All are welcome!

报告人简介：赵永强，浙江西湖高等研究院和西湖大学研究员。博士毕业于美国维斯康星大学麦迪逊分校。先后在加拿大滑铁卢大学和CRM数学研究所做博士后研究。回国前为德国马克斯普朗克研究所访问学者。研究方向是数论与算术几何，具体为算数统计，数的几何，数域类群，代数簇上有理点和整点的分布。