Expressive curves - Sergey Fomin

Stony Brook Mathematics Colloquium

Sergey Fomin, University of Michigan
October 8, 2020

We call a real plane algebraic curve C expressive if its defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of C. We give a necessary and sufficient criterion for expressivity (subject to a mild technical condition), describe several constructions that produce expressive curves, and relate their study to the combinatorics of planar bi-colored graphs, their quivers and links. This is joint work with E. Shustin.

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