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Euler characteristic of the space of real irreducible multivariate polynomials and binary expansions

Trevor Hyde (Chicago)
Tuesday, February 23, 2021 - 2:30pm
via Zoom
Trevor Hyde

Consider the space of degree d polynomials in n variables with real coefficients that are irreducible over $\mathbb R$. In this talk, I will show how the compactly supported Euler characteristic of this space has a simple expression in terms of the digits of the binary expansion of the number of variables $n$.

The talk will start with a pre-seminar at 2pm:

Title: Point counts, Euler characteristics, and the field with -1 elements.

Abstract: In this preliminary talk, I will explain how the compactly supported Euler characteristic may be thought of as a natural topological extension of cardinality, how that relates to point counts of a variety over finite field, and why it's useful to think of R as the field with -1 elements.

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