PhD 2010, MIT
Professor Kottke studies geometric moduli spaces and topological invariants, especially those involving non-compact and singular spaces, using the analysis of partial differential equations. He specializes in methods of geometric microlocal analysis, index theory and analysis on manifolds with corners. He is especially interested in problems set within the intersection of analysis, geometry and topology, and in problems arising from mathematical physics, particularly gauge theory and string theory.
Writing in Mathematics
Kottke, C. and Rochon, F. “Low energy limit of the resolvent of some fibered boundary operators.”
Communications in Mathematical Physics 390, (2022): 231-307.
Kottke, C. and Melrose, R.. “Bigerbes.”
Algebraic and Geometric Topology 21, no. 7, (2021): 3335-3399.
Kottke, C. “Functorial compactification of linear spaces.”
Proceedings of the AMS 147 no. 9, (2019): 4067-4081.
Kottke, C. and Singer, M. “Partial compactification of monopoles and metric asymptotics.”
Memoirs of the AMS, to appear.
Kottke, C., “Blow-up in manifolds with generalized corners.”
International Mathematical Research Notices 2018, no. 8, (2018): 2375-2415.