I am a Postdoctoral Fellow in the Mathematics Department at Stanford University. Before that I was a Visiting Assistant Professor at the CUNY Graduate Center. I am interested in applications of algebraic topology to various moduli spaces and configuration spaces appearing in symplectic geometry, algebraic geometry and gauge theory. I am especially interested in homological stability, representation stability, factorization homology and the topology of configuration spaces.
Email: jkmiller at stanford dot edu
Office: 383A, Building 380, Stanford, California, 94305.
I received my PhD from Stanford University in 2012 under the supervision of Ralph Cohen.
Publications and Preprints
- Representation stability for homotopy groups of configuration spaces with Alexander Kupers, Journal für die reine und angewandte Mathematik (to appear).
- En-cell attachments and a local-to-global principle for homological stability with Alexander Kupers.
- Improved homological stability for configuration spaces after inverting 2 with Alexander Kupers. Homology, Homotopy and Applications (to appear).
- Homological stability for symmetric complements with Alexander Kupers and TriThang Tran, Transactions of the American Mathematical Society (to appear). Note that this paper subsumed: Homological stability for complements of closures with Alexander Kupers.
- Homological stability for topological chiral homology of completions with Alexander Kupers.
- Some stable homology calculations and Occam's razor for Hodge structures with Alexander Kupers, Journal of Pure and Applied Algebra, 218 (2014), no. 7, 1219-223.
- Scanning for oriented configuration spaces with Martin Palmer. Homology, Homotopy and Applications (to appear).
- A twisted homology fibration criterion and the twisted group-completion theorem with Martin Palmer, Quarterly Journal of Mathematics (to appear).
- Localization and homological stability of configuration spaces with Martin Bendersky, Quarterly Journal of Mathematics, 65 (2014), no. 3,807-815.
- The topology of the space of J-holomorphic maps to CP^2, Geometry and Topology (to appear).
- Nonabelian Poincare duality after stabilizing, Trans. Amer. Math. Soc. 367 (2015), no. 3, 1969–1991.
- Homological stability properties of spaces of rational J-holomorphic curves in P^2, Algebraic & Geometric Topology, 13 (2013), no.1, 453-478.
Math 115 at Stanford University (website on Coursework