Mathematics Seminar at ICTP - this week

[Math]

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


Thursday, 23 August at 15:00 hrs.


Professor Igor V. Artamkin
(MIREA, Moscow, Russia)

"Colored graphs, Burgers equation and Hessian conjecture"

Generating function for colored graphs with tails satisfies a system of
partial differential equations generalizing the Burgers equation. This
system of differential equations admits an explicit recurrent solution
in terms of genus expansion . The corresponding system of  differential
equations for the initial term of the genus expansion is equivalent to a
functional equation concerning the inversion problem for certain formal
power series. This solution immediately provides the Bass-Connell-Wright
Tree Inversion Formula which was invented (in quite different terms) in
1982 in connection with the Jacobian Conjecture. At the same time
consideration of these equations provides some other recent developments
in the Jacobian Conjecture by W. Zhao and D. Wright.


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