报告题目：

1. Category of quantum groups over p-adic fields.

2. p-adic Hopf algebras

报告人：林宗柱 教授，美国Kansas州立大学

报告时间：

1. 2016年5月31日（星期二）下午4:00

2. 2016年6月1日（星期三）下午4:00

报告地点：

扬州大学瘦西湖校区数学科学学院38号楼一楼报告厅

主办单位：

扬州大学数学科学学院

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报告人简介：

林中柱教授：美国Kansas州立大学终生教授，博士生导师，主要从事代数表示论的研究，在美国麻省大学师从李代数名师Humphrey教授。林宗柱教授曾在美国国家自然科学基金会担任要职，是活跃在代数群、量子群表示理论研究领域的重要数学家。在Trans. Amer. Math. Soc，Contemp. Math，Invent. Math，Communications in Mathematical Physics等国际顶尖学术期刊上发表学术论文数十篇，标志性成果包括著名的Lin-Nakano定理。出版学术著作5部，并组织过多次国际会议,产生很大影响。现为《中国科学》等重要国际期刊的编委。

报告摘要：

1.The category O of the hyper algebra of an algebraic group over an algebraically field of characteristic p>0 having all irreducible representations parametrized weights with p-adic integer coefficients. To describe the Kazhdan-Lusztig theory of this category, representation theory of quantum groups over a field at p^r-th roots of 1 is needed with all irreducibles parametrized by weights with p-adic integer coefficients. In this talk, I will discuss how the construct such quantums and the associated category both in the generic case and in roots of 1 case. In this case only $p^r$-th roots can exists for such theory. The rational representation theory of this Hopf algebra is still the same as over complex number fields, but the category O can be quite different. I will discuss the properties of this category O as well as Kazhdan Lusztig theory. This is part of a joint project with Ming Fang.

2. This is a preliminary discussions of a possible theory of p-adic Hopf algebras. Given a complete discrete valuation field K with comlete valuation ring A and normalized generator p of the maximal idea, associated is a projective system A_n=A/p^n. A p-adic Hopf algebra is an Hopf algebra object in the Artin-Ree category. I will first introduce the Artin-Ree category, which is a tensor category and discuss the Hopf algebra objects as well as cohomology theory of the Hopf algebra objects. The main motivation of such object is to relate the Hopf algebra in the category of constructible p-adic sheaves over an algebraic variety over a field of positive characteristics different from $p$. This is an analog of Serre's l-adic representation theory of Galois groups。