Speaker: Alexey Ovchinnikov, Queens College (CUNY)
Title: Complexity of elimination for systems of differential equations
Date: May 3, 2016
Place: 1314 Warren Weaver Hall
Time: 6-7pm
Abstract:
We will discuss complexity bounds for the effective Nullstellensatz
for systems of polynomial PDEs. These are uniform bounds for the
number of differentiations to be applied to all equations of a system
of PDEs in order to discover algebraically whether it is consistent
(i.e., has a solution in a field). The bounds are functions of the
degrees and orders of the equations of the system and the numbers of
dependent and independent variables in them. Among several bottlenecks
in this problem is calculation of a projection of a variety. We will
also discuss another approach to simplifying systems of polynomial
PDEs, which avoids this bottleneck, as well as the associated
complexity bounds.