Title:Manin's Conjecture for a Class of Singular Hypersurfaces

Keynote Speaker:Wu Jie

Abstract: Let $n$ be a positive multiple of $4$ or $n=2$. In this talk, we shall show how to establish an asymptotic formula for the number of rational points of bounded height on singular cubic hypersurfaces $S_n$ defined by $$x^3=(y_1^2 + \cdots + y_n^2)z, $$ by analytic method.

This result is new in two aspects: first, it can be viewed as a modest start on the study of density of rational points on those singular cubic hypersurfaces which are not covered by the classical theorems of Davenport or Heath-Brown; second, it proves Manin's conjecture for singular cubic hypersurfaces $S_n$ defined above.

(Joint works with Regis de la Breteche, Kevin Destagnol, Jianya Liu, Yongqing Zhao)

Speaker Introduction:Wu Jie is a first-grade researcher at the Centre National de la Recherche Scientifique (CNRS) and doctoral supervisor at the Université Paris-Est (Universite Paris XII Val de Marne). In 1990, he received his doctoral degree from the University of Paris XI, worked at CNRS and mainly studied the analytic number theory. In 2011, he was introduced as a high-level overseas innovative talent in Shandong Province and won the title of "Taishan Scholar Overseas Specially-invited Expert". Professor Wu Jie mainly studies the distribution of prime numbers, exponential sum, modular form, and L-function. So far, he has published more than 80 papers in international mathematical publications.

Inviter:Lyu Guangshi, professor in School of Mathematics

Time:10:10-11:10 on June 14 (Friday)

Location:Hall 1032, Block B, Zhixin Building, Central Campus

Hosted by: School of Mathematics, Shandong University