Logic Seminar
William Simmons
UIC
Identifying complete differential varieties
Abstract: In classical algebraic geometry, the role of compactness is played by the
property of completeness: if $V$ and $W$ are algebraic varieties, then $V$
is complete if the projection $V\times W \rightarrow W$ is a closed map
with respect to the Zariski topology. The fundamental theorem of
elimination theory asserts that projective varieties are complete. What
happens with differential varieties, i.e., solution sets of differential
equations over
differential fields? We discuss several approaches to the problem, with
our main focus being a positive quantifier elimination test of van den
Dries that was adapted to a differential valuative criterion by Pong.
tea at 2:30 in 300
Tuesday February 28, 2012 at 4:00 PM in SEO 427