How to count zeros arithmetically?
-- Jesse Kass, January 29, 2016

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A celebrated result of Eisenbud-Kimshaishvili-Levine computes the
local degree of a smooth function f : R<sup>n</sup> &rarr; R<sup>n</sup> with
an isolated zero at the origin as the signature of the degree
quadratic form. We prove a parallel result computing the
A<sup>1</sup>-local degree of a polynomial function with an isolated
zero at the origin, answering a question posed by David Eisenbud in
1978. This talk will present this result and then discuss applications
to the study of singularities if time permits. This is joint work with
Kirsten Wickelgren.