# Mathematics Colloquia and Seminars

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### On the Dirac operator approach to the quantization commutes with reduction problem

**QMAP Seminar**

Speaker: | Nigel Higson, Penn State |

Location: | 3106 MSB |

Start time: | Mon, Oct 28 2013, 4:10PM |

The "quantization commutes with reduction" phenomenon was first explored by Guillemin and Sternberg within the context of Kahler geometry. A great deal has been written on the topic since then, often with the goal (successfully achieved) of broadening the context to symplectic geometry or beyond. But after explaining the problem I want to return to the Kahler context and examine within those confines the remarkable Dirac operator proof of Tian and Zhang of the general quantization commutes with reduction theorem in symplectic geometry. I want to show how general argument simplifies considerably in the Kahler case, and I hope I can thereby make clear the power and elegance of the Tian-Zhang approach.

Joint with Math Physics seminar