KTH/SU Mathematics
Colloquium
22 February
2006
Avgust Tsikh,
Krasnoyarsk
Amoebas and
multidimensional difference
equations
ABSTRACT
We use the language
of amoebas of algebraic hypersurfaces to get a multidimensional
analog of the fact that all roots of a univariate polynomial have
distinct moduli.
This translation allows us to obtain a
multidimensional analog of the classical result on the asymptotics
of solutions to a difference equation due to H.~Poincare.
Restrictions in applicability of the latter result are closely
related to possible generalizations of Pick's formula relating the
area and the number of integer points in a polygon.