首师大数论组讨论班（2016-06-17）

[SHUN TANG]

诸位好，本学期首都师范大学第四次数论与代数几何讨论班（两个报告）将于本月中旬举行：

时间：2016年6月17日 周五 下午 15：30--16：30--17：30
地点：首都师范大学北二区教学楼133教室（此校区位于西三环紫竹桥南首师大北一区的街对面，走一个过街天桥即到）

报告人一：Prof. Emmanuel Peyre（University of Grenoble, France）

题目：The upgraded version of Batyrev-Manin program

摘要：From the point of view of Batyrev-Manin program about rational points of bounded height, accumulating subspaces hinder the equidistribution of points. Slopes à la Bost enable one to select points the distribution of which ought to be more uniform. This leads to a new version of empiric formulae which is compatible with the example of Batyrev and Tschinkel.

报告人二：李涵 博士 （Weslyan University, USA）

题目：Masser’s conjecture on equivalence of integral quadratic forms

摘要：A classical problem in the theory of quadratic forms is to decide whether two given integral quadratic forms are equivalent. Stated in terms matrices the problem is to determine, for given symmetric n-by-n integral matrices A and B, if there is a unimodular integral matrix X satisfying A=X’BX, where X’ is the transpose of X. For definite forms one can construct a simple decision procedure. Somewhat surprisingly, no such procedure was known for indefinite forms until the work of C. L. Siegel in the early 1970s. In the late 1990s D. W. Masser conjectured for n at least 3, there exists a polynomial search bound for X in terms of the heights of A and B. In this talk we shall discuss our recent resolution of this conjecture based on a joint work with Professor Gregory A. Margulis.

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祝好！

唐舜

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Shun TANG

School of Mathematical Sciences
Capital Normal University
No. 105, West 3rd Ring North Road
100048, Beijing
P. R. China