Universal entire curves in projective spaces with slow growth

讲座时间 Datetime: 2023年8月7日，星期一， 15:00-17:00

地点 Venue: 海琴二号A457

报告人 Speaker: 陈张弛 博士后

单位 Affiliation: 中科院晨兴数学中心

主持人Host：邵国宽 副教授

报告摘要 Abstract:

In 1929, Birkhoff constructed some universal entire functions. An entire function h  is universal if any entire function g can be approximated by translations of h, in the topology of uniform convergence on compact sets.

The Nevanlinna characteristic function measures complexity of a transcendental entire function. Dinh-Sibony in their problem list (Problem 9.1) asked the minimal growth of the Nevanlinna characteristic function of universal entire maps in C^1 and P^1.

At first glance, universal entire functions looks highly transcendental and highly complicated. However, in the recent work with Song-yan Xie and Dinh Tuan Huynh, we proved that the existence of universal entire curves in any n-dim projective spaces with growth slower than any transcendental growth rate.

Our idea is motivated by Runge’s approximation theorem and the theory of Oka manifolds. I will also present some open problems.

报告人简介：

陈张弛，中科院晨兴数学中心博士后，15年本科毕业于清华大学，21年博士毕业于巴黎萨克雷大学（巴黎第十一大学）。主要研究多复变函数论、全纯叶状结构、微分不变量理论等。目前已在J. Geom. Anal.，Ergodic Theory Dynam. Systems.，Linear Algebra Appl.等期刊发表或接收7篇论文。曾担任法国青年数学联赛决赛评委。主持博士后面上基金一项。