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

A celebrated result of Eisenbud-Kimshaishvili-Levine computes the local degree of a smooth function f : Rn → Rn with an isolated zero at the origin as the signature of the degree quadratic form. We prove a parallel result computing the A1-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.