Fermat functional equations revisited
Speaker:Prof. Tuen Wai NG
Professor
The University of Hong Kong
Hong Kong
Date & Time:23 Nov 2016 (Wednesday) 16:00 - 17:00
Venue:E11- 1038
Organized by:Department of Mathematics

Abstract

The problem of the existence of transcendental meromorphic or entire solutions for the Fermat functional equation f^n+g^n+h^n=1 was first studied by Walter Hayman in 1984. By the work of Fred Gross, Mark Green, Gary Gundersen, Kazuya Tohge and others, it is known that meromorphic (entire) solutions exist for n < 7 (n < 6). While Hayman showed that no meromorphic (entire) solution exists when $n> 8$ ($n > 6$) by Cartan's version of Nevanlinna theory. In this talk we will revisit this problem and try to understand Hayman's results from a more geometric point of view through the applications of jet differentials. We shall also consider the related problems for the generalized Fermat functional equation f^n+g^m+h^l=1. This is a joint work with Sai-Kee Yeung.

Biography

Prof. Ng is currently a Professor of the University of Hong Kong. Prof Ng's main research area is complex analysis, in particular factorizations of mermorphic functions, complex dynamics, complex differential equations and geometry of polynomials. Through his teaching, he also has a side interest in game theory and mathematical biology. He is on the editorial board of Bulletin of the Australian Mathematical Society.