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Rafe Mazzeo: Lectures

April 11, 2018
TITLE: Analysis of elliptic operators on complete spaces with asymptotically regular collapsing geometry

ABSTRACT: Elliptic theory for asymptotically cylindrical and asymptotically conical spaces is now classical and can be approached in many ways. When dealing with slightly more intricate geometries at infinity it is often helpful or even necessary to use more sophisticated tools. This talk will discuss a general and systematic theory which leads to sharp mapping results for ALF/ALG type metrics and prospects for a similar theory for singular fibrations over QAC spaces.

April 10, 2018
TITLE: The large-scale structure of the Hitchin moduli space

ABSTRACT: The moduli space of solutions to the Hitchin equations on a Riemann surface carries a natural hyperKaehler metric, and questions and conjectures about its asymptotic structure have emerged out of the physics literature. There has been a lot of progress on this recently. I will discuss recent results, showing why this space might reasonably be called QALG.