Chris Kottke, Mathematics, New College of Florida

Employment

2016-present: Assistant Professor of Mathematics, New College of Florida.

2013-2016: Research Instructor, Mathematics Department, Northeastern University.

2010-2013: Tamarkin Assistant Professor, Mathematics Department, Brown University.

PhD 2010, MIT. Student of Richard Melrose.

Interests

Global, geometric and microlocal analysis; gauge theory, moduli spaces and loop spaces.

Research

My research broadly concerns geometric moduli spaces and topological invariants, especially those involving noncompact and singular spaces, with an approach through the analysis of partial differential equations. I specialize in the methods of geometric microlocal analysis (pseudodifferential and Fourier integral operators on manifolds), index theory and analysis on manifolds with corners. I am 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.

Here is a full research statement, and a curriculum vitae.

My current research projects include

Previously, I did some work in applied mathematics on perturbation theory for anisotropic dielectric interfaces, and before that, on large scale parallel numerical simulation of fluid dynamics.

Publications and preprints

List of my arXiv preprints

Notes & other writings