Fields Geometric Analysis Colloquium

We study degenerations of Riemannian manifolds converging to orbifolds and analyse the behaviour of Dirac operators along smooth Gromov–Hausdorff resolutions, where classical elliptic theory breaks down. Using weighted analysis and geometric decompositions, we establish a uniform Fredholm theory, including a gluing description of kernels and an index additivity formula. We then apply this framework to Spin(7) geometry, where orbifold limits naturally appear at the boundary of the moduli space of torsion free Spin(7)-structures. By incorporating resolution data, we enlarge the moduli space to include these limits and effectively fill in its boundary. This perspective connects to a Spin(7) analogue of the crepant resolution conjecture and provides a geometric interpretation of the associated obstructions.

http://www.fields.utoronto.ca/activities/25-26/geometric-analysis-colloquium