吴文俊数学重点实验室动力系统系列讲座之十

报告人：王之任  
       耶鲁大学数学系，Gibbs Assistant Professor

报告1
报告题目：The x2,x3 problem and its extensions

报告时间：2012年7月17日下午16:00-17:00

报告地点：管理科研楼1318教室

摘要: This talk will mention the history of Furstenberg's theorem
and conjecture, and various higher dimensional analogues of them.

报告2
报告题目：Dynamical studies of Euclidean minima

报告时间：2012年7月19日下午16:00-17:00

报告地点：管理科研楼1318教室

摘要：The Euclidean minimum M(K) of a number field K is an important numerical
 invariant that measures to what extent K is norm-Euclidean. It is the
supremum of the Euclidean spectrum Spec(K) of K. The computability of
M(K) as well as its isolatedness in Spec(K) has been much studied in
computational number theory. In this talk, we will discuss how previous
works by Lindenstrauss and Wang on topological rigidity of Z^r-actions
by toral automorphisms can be applied to such studies. In particular, we
will give an upper bound for the computational complexity of M(K) for
 non-CM fields of unit rank strictly greater than 1. For CM fields of
unit rank strictly greater than 2, we show that M(K) is attained and
isolated in Spec(K). Combined with Cerri's work, our result implies M(K)
can be computed in finite time for all K of degree 7 or higher.

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          中科院吴文俊数学重点实验室

 
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