Mathematical logic and its applications in number theory
Time: Tue, 25 Jun 2019, 13:30-15:05
Place: Third lecture room at Jinchunyuan West Building, Tsinghua University
Speaker: Jinbo Ren (University of Virginia)
Abstract:
A large family of classical problems in number theory such as:
a) Finding rational solutions of the so-called trigonometric Diophantine equation F(cos 2πxi, sin 2πxi)=0, where F is an irreducible multivariate polynomial with rational coefficients;
b) Determining all λ∈ℂ such that (2, (2(2-λ))1/2) and (3, (6(3-λ))1/2) are both torsion points of the elliptic curve y2=x(x-1)(x-λ);
can be regarded as special cases of the Zilber-Pink conjecture in Diophantine geometry. In this talk, I will explain how we use tools from mathematical logic to attack this conjecture. In particular, I will present a series partial results toward the Zilber-Pink conjecture, including those proved by Christopher Daw and myself.
This talk is an expanded version of the one I gave during ICCM.