首师大数论组讨论班（2016-04-22）

[SHUN TANG]

诸位好，本学期首都师范大学第三次数论与代数几何讨论班将于本周举行：

时间：2016年4月22日 周五 下午 16：30--17：30
地点：首都师范大学北二区教学楼513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：Prof. Emmanuel Peyre（University of Grenoble, France）

题目：Curves Statistics

摘要：The analogy between number fields and function fields of curves is a truism of arithmetic geometry. It is therefore natural to look for links between the asymptotic behaviour of points of bounded height on a variety and the geometry of the moduli space of morphisms of high degree from a curve to this variety. On the geometric side, this leads to a new approach for the understanding of curves on split flag varieties or toric varieties.

请将此信息转发给其他感兴趣的老师和学生，期待与大家相会！

祝好！

唐舜

--

Shun TANG

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

[xu...@math.ac.cn]

诸位：

下周三下午（9月28日）2：30-5：30 讨论班，安排下面三个报告，欢迎参加！

时间：2016年9月28日 （周三） （2：30-5：30）。
地点：首都师范大学北二区教学楼509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）

1. 报告人：Xuanyu Pan (Max-Planck Institute) (2:30-3:30)

Title: Griffiths Groups and Chow Groups

Abstract: In this talk, I will talk about my work on the Griffiths groups of Fano varieties of lines and the second Chow groups of "3-Fano" hypersurfaces. In fact, we give a positive answer to a question of Professor Voisin in some cases.More precisely, we show that the rst Griffiths groups of Fano varieties of lines of "2-Fano" hypersurfaces are trivial and the second Chow groups of "3-Fano" hypersurfaces are torsion-free and of rank one. The proof is based on the Tsen-Lang theorem, the moduli space of stable maps, the bend-and-break theorem and the geometry of quadric surfaces in a hypersurface.

2. 报告人：赵永强 （University of Waterloo) (3:30-4:30)

Title: On the distribution of  rational points on a class of singular cubic hypersurfaces.

Abstract: In this talk, we report some recent results on the distribution of rational points on a class of singular cubic hypersurfaces, which can be viewed as some very modest addition to Davenport's work on cubic forms and to high dimensional Manin's Conjecture. This is a joint work with Jianya Liu and Jie Wu.

3. 报告人：杨磊（University of Hebrew) (4:30-5:30)

Title: Equidistribution of curves in homogeneous spaces and Diophantine approximation for matrices

Abstract: We consider an analytic curve in a homogeneous space, translated by a particular diagonal subgroup. Given a geometric condition, we want to show the translates of the curve tend to be equidistributed in the homogeneous space. In this talk, we will discuss the result for the case when the space admits an action of SL(m+n, R), and its application to Diophantine approximation for m by n matrices. This is a joint work with Nimish Shah.

祝好！

徐飞

[xu...@math.ac.cn]

诸位：

周二下午（10月11日）4：30-5：30 讨论班，欢迎参加！

时间：2016年10月11日 （周二） （4：30-5：30）。

地点：首都师范大学北二区教学楼515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：赵以庚（University of Regensburg）

题目: Etale duality for p-torsion sheaves on semistable schemes

摘要: In this talk, we will introduce the relative logarithmic de Rham-Witt sheaves on a semistable scheme X over a local ring of positive characteristic p, and study duality theorems. As an application, we will define a filtration on the abelianized etale fundamental group of open complement of a simple normal crossing divisor on X. In a special case, this filtration coincides with higher ramification groups in local class field theory.

祝好！

徐飞

[xu...@math.ac.cn]

诸位：

周五下午（10月21日）4：30-5：30 讨论班，欢迎参加！

时间：2016年10月21日 （周五） （4：30-5：30）。

地点：首都师范大学北二区教学楼508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：刘青教授（法国 Bordeaux 大学）

题目: New points in algebraic varieties

摘要: Let g be a positive integer. Given a finite extension
of fields L/K, we consider the question whether there
exists a projective curve X of genus g over K with a
point with coordinates in L (but not in any subextension
of L). It turns out that this is always possible if
the degree of L over K is small enough with respect to g.
This question is related to an explicit bound in a
finiteness result of Caporaso-Harris-Mazur. This is a
common work with Dino Lorenzini.

（报告内容以这个通知为准）

 

祝好！

徐飞

[xu...@math.ac.cn]

诸位：

欢迎参加下周算术几何讨论班。

报告人：杜托平博士（西北大学）

时间：2016年11月23日（星期三）上午 10：30-11：30

地点：首都师范大学北二区教学楼508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）

题目： Arithmetic Siegel-Weil formula on X_{0}(N).

摘要: Our work is a case of Kudla's program. Kudla, Rapoport and Yang gave some cases on division Shimura curves. In this talk, we construct an arithmetic theta function on arithmetic surface X_{0}(N). The degree of this function is the value of an Eisenstein series.The height  of it is the derivative of this Eisenstein series. 


祝好！

徐飞

[xu...@math.ac.cn]

诸位：

欢迎参加本年度最后一个讨论班。

报告人：王楠博士（沈阳师范大学）

时间：2016年12月28日（周三），下午4：30-5：30

地点：首都师范大学北2区教学楼508教室

报告题目：

Del Pozo's lower bound of Weierstrass weight

报告摘要：

In this talk, we consider the Weierstrass point on smooth algebraic
curve and its weight. Firstly, I will introduce a lower bound of the
(Weierstrass) weights of fixed points of automorphisms on a algebraic
curve over the complex number field, which is given by Del Pozo in
2006. Then I will provide necessary and sufficient conditions for when
this lower bound is attained, which is a joint work with Sakai Fumio
and Kawasaki Masumi. And I will also discuss some other related
topics.

祝好！

徐飞