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### Degenerating solutions of some gauge field equations

**Geometry/Topology**

Speaker: | Rafe Mazzeo, Stanford University |

Location: | 2112 MSB |

Start time: | Thu, Nov 13 2014, 3:10PM |

I will discuss some recent work about a new construction of 'large solutions' to Hitchin's equations on a Riemann surface. One goal is to obtain a good understanding of the geometry of the ends of the moduli space of solutions to these equations, and in particular to find ways to vindicate a beautiful proposal by Gaiotto-Moore-Neitzke about the asymptotic structure of the L^2 metric on this moduli space using geometric analytic methods. If time permits, I will talk about ramifications of this for the Kapustin-Witten equations.