Speaker：Min Ru (University of Houston)

Time：2021-03-30 10:00

Location：Tencent Meeting ID：327 386 309（No Password）

Abstract:

The Diophantine approximation is one of the important branches in number theory. The word Diophantine refers to the mathematician of the 3rd century, Diophantus of Alexandria, who was one of the first mathematicians to introduce symbolism into algebra. The Diophantine approximation deals with the approximation of algebraic numbers, which was measured by the approximation exponent d. Based on the earlier works of Thue-Siegel-Dyson, Klaus Roth in 1955 obtained the best result with exponent 2 which is in some sense the best possible. Roth was later awarded the Fields Medal because of this work.  Later W. Schmidt extended Roth's work to several variables. Recently there have been some new and important developments in extending Schmidt's result, due to the works of Corvaja-Zannier, Evertse-Ferretti and Ru-Vojta. In this talk, I will discuss such developments, based on the recent paper (joint with Paul Vojta) published in Amer. J. Math., as well as a recent submitted manuscript with Vojta.