**高端引智Grigor Barseghyan 院士系列讲座一**

时间：2017年4月12日周三和4月13日周四下午2点到4点

地点：广州大学理学实验楼314室 综合性学术讲座

**Introductory Lecture**

**Three novel trends in complex analysis complementing Nevanlinna- Ahlfors theories. Applications to complex differential equations.**

**Barsegian Grigor**

**Abstract**

In this lecture, we presented some results related to arbitrary meromorphic functions in a given domain or in the complex plane, which were obtained comparatively recently.

Meromorphic functions in the complex plane were widely studied in the classical theories: since 1890s "French direction" (Picard, Julia, Borel, Milloux results) and since 1920s Nevanlinna value distribution theory (Similar results are also true for functions in the unit disk which satisfy some additional restriction to the growth).

Much less were studied arbitrary meromorphic functions in a given domain: in the 19^{th}century the basic results were established by Cauchy; In the 20^{th}century we mentioned just the fundamental theorems in Ahlfors theory of covering surfaces (1935).

Since late 1970s some other results of the same generality were established. They can be attributed mainly to three new topics (trends): Gamma-lines, proximity property and universal version of value distribution.

These topics reveal some novel phenomena; Meantime, they complement also the mentioned classical studies.