Presented By: Representation Stability Seminar - Department of Mathematics
Schmidt rank/strength and the singular locus
Amichai Lampert
Given a multivariate polynomial f, Schmidt rank/strength is a quantity defined algebraically which measures its non-degeneracy. In 1985 Schmidt introduced this quantity and showed that over the complex numbers it's closely related to a geometric quantity measuring non-degeneracy: the codimension of the singular locus of (f=0). Ananyan and Hochster proved a similar relationship holds for algebraically closed fields of arbitrary characteristic, but with very weak bounds. I will present a recent result giving strong bounds in any characteristic which doesn't divide the degree of f, and discuss upcoming work on the case deg(f) = char(k) = p.
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