数論幾何学セミナー:Zeta Functions and Their Zeros

開催日時
2014年   7月 22日 10時 00分 ~ 2014年   7月 23日 16時 00分
場所
北海道大学理学部3号館413(7/22) / 3号館307(7/23)
講演者
Lin Weng(九州大学)
 
Abstract :

In this lecture series, we will mainly report some recent developments on zeta functions for function fields and their zeros, particularly, on motivic Euler product  and motivic Tamagawa number conjecture, (uniforming arithmetic theory of Harder-Narasimhan and geometric theory of Atiyah-Bott,) on the Riemann hypothesis for zetas of elliptic curves and special uniformity of zeta functions, (claiming that rank n non-abelian zeta and SL_n zeta coincide,) on Cohen-Lenstra heuristics for Selmer groups of elliptic curves , on the parabolic reduction, stability and masses conjecture, (counting total and semi-stable principal bundles on curves,) on distributions of zeros, and on various Eisenstein periods, among others. Eight lectures will be distributed as follows:

1. Motivic Euler product and its applications

2. Special uniformity of zeta functions  (jointly with Zagier)

3. Riemann Hypothesis for elliptic curves  (jointly with Zagier)

4. Distributions of zeros

5. Cohen-Lenstra heuristics for elliptic curves  (jointly with Sugahara)

6. Parabolic reduction, stability and masses

7. Eisenstein periods for number fields

8. Eisenstein periods for loop groups

関連項目

研究集会・セミナー・集中講義の一覧へ