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Rafe Mazzeo: Lectures

June 6, 2022
TITLE: An approach to analysis on stratified spaces, with a view toward
spectral invariants

ABSTRACT: This will be a survey of old material, and focusing on case studies, of how the tools of geometric microlocal analysis may be applied to study some linear and nonlinear elliptic and parabolic problems. A motivation for presenting this here is the natural appearance of spaces with iterated edge singularities in the study of special holonomy. I will discuss, in particular, some ideas that have been useful in understanding global spectral invariants on singular and degenerating manifolds, where it is necessary to understand fine asymptotic structure.

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.