Seminar on Algebraic Geometry: Zeta Functions and Their Zeros

2014-7-22 10:00 - 2014-7-23 16:00
Faculty of Science Building #3 Room 413(22JUL) / #3 Room 307(23JUL)
Lin Weng(kyushu University)
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