Return to Colloquia & Seminar listing
Sparse polynomial systems given by graphs
Student-Run Research| Speaker: | Dr. Karin Gatermann, FU Berlin, ZIB, DFG |
| Location: | 593 Kerr |
| Start time: | Wed, May 9 2001, 1:10PM |
Description
We study a system of polynomial equations arising in modelling
chemical reactions. The coefficients and the exponents
of the polynomials are given by a weighted directed graph
(some chemical reactions) and a weighted bipartite graph.
For the study of stability of solutions special Liapunov functions are used.
That means the optimization function is to be found which attains its
minimum at the solution.
I will explain the benefits of a certain convex polyhedral cone which
comes together with a deformed toric variety. For the computation of the
minimal generators of the cone one may of course use the simplex
algorithm because under an additional constraint the cone gives the
feasible set of a linear optimization problem. But in this particular
situation many generators are given by positive circuits of the directed graph
with consequences.
In the second part of my talk I will generalize the counting
of positive solutions of a sparse polynomial system to the counting
of stable positive solutions.