William Simmons : Identifying complete differential varieties

Posted by , part of the Logic Seminar.

At

Feb. 28, 2012, 4 p.m.

In

SEO 427

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.

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