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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 (pseudodifferential and Fourier integral operators on manifolds), 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.
Advanced Linear Algebra
“Dimension of monopoles on asymptotically conic 3-manifolds”,
Bulletin of the LMS, vol. 47, no. 5, (2015), pp. 818-834.
“Loop-fusion cohomology and transgression” (with R. Melrose),
Mathematical Research Letters, vol. 22, no. 4, (2015), pp. 1177-1192.
“A Callias-type index theorem with degenerate potentials”,
Communications in PDE, vol. 40, no. 2, (2015), pp. 219-264.
“Generalized blow-up of corners and fiber products” (with R. Melrose),
Transactions of the AMS, vol. 367, no. 1, (2015), pp. 651-705.
“An index theorem of Callias type for pseudodifferential operators”
Journal of K-Theory, vol. 8, no. 3, (2011), pp. 387-417.