A new theory of permutation polynomials




报告摘要:In this talk we present a new approach to the study of permutation polynomials over finite fields, which makes use of algebraic geometry, elliptic curves, algebraic number theory, and serious group theory. We use this approach to produce many new classes of permutation polynomials, to determine all permutation polynomials within several classes of polynomials, and to resolve nearly all conjectures in the subject. In addition we explain some new types of questions arising from our approach. This is joint work with Michael Zieve.

专家简介:丁治国,现为美国密歇根大学访问学者,曾就职于国防科技大学。丁治国于中国科学院获得博士学位,研究方向为数论,长期与国际知名数学家MichaelZieve合作,在有限域的算术领域做出了一系列工作,研究成果发表于Proc. Lond. Math. Soc.,Int. Maht. Res. Not.等多个国际著名期刊。