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The Hilbert scheme of points in affine space

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KA2W01 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

I will discuss the Hilbert scheme of d points in affine n-space, with some examples. This is a “configuration space” with a simple description as a space of ideals in a polynomial ring, but it has been largely mysterious for n greater than 2. We determine the motivic homotopy type of the Hilbert scheme in a range of dimensions, using the homotopy theory of algebraic stacks. Many questions remain. (Joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Maria Yakerson.)

This talk is part of the Isaac Newton Institute Seminar Series series.

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