学术交流

2017年河南大学复分析研讨会

 时间 报告人 报告题目 上午 8:20-8:30 冯淑霞 数学学院院长 致开幕词 8:30-9:30 汝敏 休斯顿大学 Introduction   to the theory of holomorphic curves (Nevanlinna theory) 9:30-10:10 刘晓俊 上海理工大学 Normal   Family Theory and Gauss Curvature Estimate of Minimal Surfaces in Rm 10:20-10:40 茶歇 10:40-11:20 于光升 上海理工大学 Upper   Bounds of GCD Counting Function for Holomorphic Maps 11:20-12:00 李怀彬 河南大学 Topological   invariance of a strong summability condition in one-dimensional dynamics 12:00-14:30 午餐及休息 下午 14:30-15:30 嵇庆春 复旦大学 Dirac型方程与伪全纯曲线 15:30-16:10 颜启明 同济大学 On   Cartan's Second Main Theorem and Schmidt's Subspace Theorem 16:10-16:30 茶歇 16:30-17:10 黄炎 河南大学 on   hausdorff dimension of the set of nonergodic directions in the double cover   of tori 17:10-17:50 吴菊杰 河南大学 A   counterexample for polynomials are not dense in the Hilbert space 18:00-20:00 晚餐

Title: Introduction to the theory of holomorphic curves (Nevanlinna theory).

Abstract: In this talk, I'll introduce the basic techniques in the study of holomorphic curves into projective varieties. I'll also survey some past and recent development in the study of this and related areas.

1983年获得华东师范大学数学学士学位，1986年获得华东师范大学数学硕士学位，1990年获得美国诺特丹大学数学博士学位. 1990-1992年，新加坡国立大学助理教授. 1992-1995年，哈佛大学，Benjamin Peirce数学助理教授. 1996.1-1996.6 伯克利数学科学研究所研究员. 1995-1997年，休斯顿大学数学助理教授. 1997-2002年，休斯顿大学副教授.  2002年至今，休斯顿大学教授.

1993-2002年连续三次获得国家自然科学基金支持， 1998年至今连续七次获得美国国家安全局数学项目的支持，均为主持人。2006年至今担任休斯顿大学数学杂志的编委。

Title: Normal Family Theory and Gauss Curvature Estimate of Minimal Surfaces in Rm

AbstractIn this paper, we first introduce some concepts about minimal surface, Gauss map and Gauss curvature in Rm, then extend Zalcman’s principle of normality to the families of holomorphic mappings from Riemann surfaces to a compact Hermitian manifold. After that, we use this principle to derive an estimate for Gauss curvatures of the minimal surfaces in Rm whose Gauss maps satisfy some property P so called compact property, in the spirit of Bloch’s heuristic principle in traditional complex analysis. Consequently, we recover and simplify the known results about value distribution properties of the Gauss map of minimal surfaces in Rm.

TitleUpper Bounds of GCD Counting Function for Holomorphic Maps

AbstractWe give upper bounds for the gcd counting function(which is an analogue for the notion of gcd in the context of holomorphic maps) in various settings. As applications, we obtain analytic dependence of entire functions from the second main theorem and multiplicative dependence under the fundamental conjecture for entire curves.

Title: Topological invariance of a strong summability condition in one-dimensional dynamics

Abstract: We say that a rational map $f:\CC\to\CC$ satisfies a strong summability condition if for each critical value $v$ of $f$ belonging to the Julia set, we have

$\sum_{n=0}^\infty|Df^n(v)|^{-\beta}<\infty$ for any $\beta>0$. We give an equivalent formulation of this property in terms of backward contracting properties of $f$. We prove that the strong summability condition is a topological invariant for rational maps with one critical point in the Julia set and without parabolic cycles. For

unimodal interval maps, we obtain that the strong summability condition is invariant under quasisymmetric conjugacy.

TitleOn Cartan's Second Main Theorem and Schmidt's Subspace Theorem

AbstractVia Vojta's dictionary, the counterpart of Cartan's second main theorem is Schmidt's subspace theorem. In this talk, we will introduce the new version of second main theorem and subspace theorem. The corresponding Wirsing type result is also considered.

Title: On hausdorff dimension of the set of nonergodic directions in the double cover of tori

Abstact:we prove that there exist the third_kind double cover of tori for which the hausdorff dimension of nonergodic directions is 1/2.

TitleA counterexample for polynomials are not dense in the Hilbert space

AbstractIt's not the case that polynomials are dense for general psh weight functions ‑ so that the corresponding Hilbert space contains the polynomials.

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