# Grigor Barsegian

## Fields of Interests:

- main field: Complex analysis (Nevanlinna value distribution theory)
- geometric functions theory
- classes of complex functions
- particularly quasiconformal mappings
- Minimal surfaces
- Algebraic Geometry
- turbulence in analysis and applications of some recent results and trends in physics
- biomathematics
- economical mathematics
- real differential equations
- complex differential equations.

Three PhD theses

Visited nearly 40 institutions, among them was visiting professor in HKUST, Hong Kong (1997, 2001); in UNED Madrid, Spain (2005); Research Fellow in ICTP, Italy (2002-2009); Research in Pairs in Oberwolfach, Germany (2009); Marie Curie Fellow in University Colledge London (2013-2015); Leading visiting professor in Guangzhow universuty, China (2017).

** Grants, appointments, invitations:**

**Plenary lectures and invited addresses (11):**

**Special sessions organized at the ISAAC Congresses.**

**Conferences, workshops organized.**

** On some new principles and trends.**

The results of a general nature related to basic concepts in mathematics (usually referred as principles) were established mostly before 20th century and quite few in 20th century. We mean here primarily such a basic concepts as arbitrary enough smooth real functions of one and two variables, plane curves and surfaces in R³, arbitrary meromorphic (particularly analytic) functions in a given domain.

**A list of more than 20 new principles and 5 new trends**

**related to the basic concepts in mathematics. References.**

*principle of angles*, see [Bars2009] (plenary lecture at the 6th ISAAC Congress;

**Shortly about five trends.**

**Trend 1**: relates to studies of oscillations, i.e. zeros, of solutions of systems of real differential equations.

**Trend 2**: relates to studies of analytic or meromorphic solutions in a given domain of complex differential equations.

**Trend 3:**relates to Gamma-lines of meromorphic functions w(z) particularly level sets of functions Rew(z).

**Trend 4**: relates to studies of the geometry of a-points of meromorphic functions w(z).

**Trend 5**: Universal version of value distribution for meromorphic functions in a given domain.

**REFERENCES**

** BOOKS, EDITED VOLUMES. **

**RESEARCH PAPERS.**