Jeremy Miller


I am an Assistant Professor at Purdue University. Before that I was a Postdoctoral Fellow in the Mathematics Department at Stanford University and 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. 

Contact Information
Email: jeremykmiller at purdue dot edu
Office: 710, 150 N. University Street, West Lafayette, IN 47907. 

Education
I received my PhD from Stanford University in 2012 under the supervision of Ralph Cohen.

Publications and Preprints
  1. Representation stability for homotopy groups of configuration spaces with Alexander KupersJournal fur die reine und angewandte Mathematik (to appear). 
  2. En-cell attachments and a local-to-global principle for homological stability with Alexander Kupers.
  3. Improved homological stability for configuration spaces after inverting 2 with Alexander KupersHomology, Homotopy and Applications (2015), no. 1, 255-266.
  4. Homological stability for symmetric complements with Alexander Kupers and TriThang TranTransactions of the American Mathematical Society (to appear). Note that this paper subsumed: Homological stability for complements of closures with Alexander Kupers
  5. Homological stability for topological chiral homology of completions with Alexander Kupers.
  6. Some stable homology calculations and Occam's razor for Hodge structures with Alexander KupersJournal of Pure and Applied Algebra, 218 (2014), no. 7, 1219-223.
  7. Scanning for oriented configuration spaces with Martin Palmer. Homology, Homotopy and Applications (2015), no. 1, 35-66. 
  8. A twisted homology fibration criterion and the twisted group-completion theorem with Martin PalmerQuarterly Journal of Mathematics, 66 (2015), no. 1, 265-284.
  9. Localization and homological stability of configuration spaces with Martin Bendersky, Quarterly Journal of Mathematics, 65 (2014), no. 3,807-815.
  10. The topology of the space of J-holomorphic maps to CP^2, Geometry and Topology (to appear). 
  11. Nonabelian Poincare duality after stabilizingTrans. Amer. Math. Soc. 367 (2015), no. 3, 1969-1991.
  12. Homological stability properties of spaces of rational J-holomorphic curves in P^2, Algebraic & Geometric Topology, 13 (2013), no.1, 453-478.
Seminars
At Stanford, I organized the Topology Progress Seminar.
At the CUNY Graduate Center, I organized the Student topology seminar and the Configuration spaces and E_n algebras seminar.

Current teaching

Past teaching
Math 113 at Stanford University.
Math 115 at Stanford University (website on Coursework).
Math 215C at Stanford University.
Math 156.2 at Hunter College.
Math 260.2 at Hunter College.