Function Field Theory

Prerequisite

Abstract Algebra, Number Field Thoery

Abstract

Algebraic Function thoery involves the study of the field extensions of transcendental degree one. In algebraic geometry, a function field correspondences to the function field of some algebraic curve. In number theory, a function field will play a role similar to that of a finite extension of the field of rational numbers. Also, the theory of function field serve as an infinite source of inspiration for a similar study of Riemann surface, as a main geometry topics in complex analysis. Several concepts of a totally analytic nature such as those of differentials, distances, and meromorphic functions may be studied from an algebraic viewpoint and are consequently likely to be translated into arbitrary fields, including fields of positive characteristic.

Lecturer Intro.

Hu chuangqiang joined Bimsa in the autumn of 2021. The main research fields include: coding theory, function field and number theory, singularity theory. In recent years, he has made a series of academic achievements in the research of quantum codes, algebraic geometric codes, Drinfeld modules, elliptic singular points, Yau Lie algebras and other studies. He has published 13 papers in famous academic journals such as IEEE Trans. on IT., Final Fields and their Applications, Designs, Codes and Cryptography. He has been invited to attend domestic and international academic conferences for many times and made conference reports.