Mathematics Seminar at ICTP - next week

[Math]

M A T H E M A T I C S   S E M I N A R S   2007


Tuesday, 12 June at 14:00 hrs.


Professor Grigor A. Barsegian
(National Academy of Sciences of Armenia)

"Geometric theory of level sets of real functions and surfaces"

Abstract:   We build a mathematical theory of level sets of  
''smooth'' real
functions and surfaces.

Similar results were obtained in the 1970s in Gamma-lines theory for an
important but particular class of harmonic functions. In turn, Gamma- 
lines
theory is similar to Nevanlinna theory of value distribution of  
meromorphic
functions.

Studies have progressed as follows. The classical Nevanlinna deficiency
relation was transferred into Gamma-lines theory and in this paper we
establish an analogous assertion for real functions and surfaces.

It is therefore becoming apparent that Nevanlinna type phenomena have  
rather
universal character in mathematics since the phenomena  now have
corresponding varieties in complex analysis, in real analysis and in
geometry.

Since the level sets admit interpretations in many applied sciences,  
one can
hope that the new theory will be useful in applications.

Note that in physics, for instance, the level set can be an
isoterm, isobar, potential line, streaming line, or a set where  
chemical,
oil, or radiation pollution have the same constant value.

VENUE:  SEMINAR ROOM (ICTP Main Building, first floor)