# Mathematics Colloquia and Seminars

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### The space of vector bundles on spheres: algebra, geometry, topology

**Colloquium**

Speaker: | Ravi Vakil, Stanford University |

Related Webpage: | http://math.stanford.edu/~vakil/ |

Location: | 1147 MSB |

Start time: | Tue, Feb 26 2019, 4:10PM |

Bott periodicity relates vector bundles on a topological space \(X\) to vector bundles on \(X \times S^2\): the “moduli space” \(BU\) of complex vector bundles is basically the same as the “moduli space” maps of a sphere to \(BU.\) I’m not a topologist, so I will try to explain an algebraic or geometic incarnation, in terms of vector bundles on the Riemann sphere. The algebro-geometric incarnation of Bott periodicity is actually motivated by important current questions in geometry. I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally. This is joint work in progress with Hannah Larson, who did the heavy lifting.