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Genus zero maps, quivers, and Bott Periodicity

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EMGW05 - Moduli stacks and enumerative geometry

We give a quiver description of the space of genus 0 parameterized maps to various Generalized Flag Varieties. In the 90s it was proven that for maps of large degree, these spaces are good homotopy approximations to the space of all continuous maps — the double loops spaces that appear in the Bott Periodicity theorem (both the 2-fold and 8-fold periodicity theorems). Our quiver description recovers Bott Periodicity in the large rank and degree limit and can thus be regarded as a finite dimensional, algebraic refinement of Bott Periodicity.  This is joint work with Ravi Vakil.

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

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