西湖数论研讨班第八期

来源:WIAS 发布时间:2018-10-13 作者: 阅读数:1305次



地点:理学研究所大楼409


1.演讲人: 南方科技大学胡勇教授

时间:10月13号上午9:00-12:00

Title:  Sums of squares in fields

Abstract:This talk will first provide a short introduction to the algebraic theory of quadratic forms over fields. Then we will focus on sums of squares in various fields with nice arithmetic properties. In particular, we will discuss upper bound results for function fields and Laurent series fields.


2.演讲人:青岛大学刘奎博士

时间: 10月13号下午1:30-4:30

题目:An application of lattice theory on counting points on curves

modulo an intege

摘要:Given an integer q and a polynomial f in Z_q[X] with

coefficients in the residue ring Z_q = Z/qZ. We will introduce recent

results of Kerr and Mohammadi and show how to estimate the number

of points on curves y^2=f(x) (mod q) by lattice theory.

 

3. 演讲人: 西北大学杜托平教授

时间:10月14号上午8:30-11:30

 

Title:Igusa’s work on higher degree form and local zeta functions

Abstract:I will recall Igusa's work on  higher degree form. Firstly, I will introduce his local zeta functions, which are related to exponential sums (mod p^m). This local zeta function is a rational function of q^{-s}. Secondly, I will recall the Siegel-Weil formula of higher degree form.

 

4. 演讲人:南昌大学胡立群博士

时间:10月14号下午13:00-16:00

Title:Counting Rational Points on Biprojective Hypersurface

Abstract: An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski open subset of the biprojective hypersurface in many variables, which is defined over the rational numbers. This confirms the Mannin conjecture for this variety.


报名链接:http://www.wias.org.cn/index.php?a=details&type=8

西湖数论研讨班介绍:http://121.196.232.36/index.php?a=detail&catid=543&id=9455&web=chinese