I am an Assistant Professor in the mathematics department at the University of Kentucky.
From 2016-2017 I was a postdoc at the University of Regensburg. From 2014-2016 I was a postdoc at the Max Planck Institute for Mathematics. From 2011-2014 I was a CLE Moore Instructor at MIT. My Ph.D. advisor was Charles Rezk at the University of Illinois at Urbana-Champaign.
I work on interactions between algebraic topology, algebraic geometry, representation theory, and arithmetic geometry. Specifically, I am interested in Morava E-theory and the relationship between chromatic heights.
This semester I am primarily working with Tobias Barthel, Dan Berwick-Evans, Peter Bonventre, Lukas Brantner, Bert Guillou, Zhen Huan, Markus Hausmann, Niko Naumann, Sune Precht Reeh, Tomer Schlank, and Chris Schommer-Pries on a variety of projects.
My work is partially supported by the National Science Foundation grant DMS-1906236. My collaboration with Tomer Schlank is partially supported by the U.S. Israel Binational Science Foundation grant 2018389. I may be contacted at nat.j.stapleton at gmail.com. My office is POT 765.
Here is my CV.
Papers
- Monochromatic homotopy theory is asymptotically algebraic, with Tobias Barthel and Tomer M. Schlank
. - Lubin-Tate theory, character theory, and power operations, to appear in the Handbook of Homotopy Theory
. - Chromatic homotopy theory is asymptotically algebraic, with Tobias Barthel and Tomer M. Schlank
. - The Balmer spectrum of the equivariant homotopy category of a finite abelian group, with Tobias Barthel, Markus Hausmann, Niko Naumann, Thomas Nikolaus, and Justin Noel, accepted by Inventiones Mathematicae
. - Excellent rings in transchromatic homotopy theory, with Tobias Barthel, Homology, Homotopy, and Applications,
2018 . - A formula for p-completion by way of the Segal conjecture, with Sune Precht Reeh and Tomer M. Schlank
. - A canonical lift of Frobenius in Morava E-theory, Homology, Homotopy, and Applications,
2018 . - Brown-Peterson cohomology from Morava E-theory, with Tobias Barthel and an appendix by Jeremy Hahn, Compositio Mathematica,
2017 . - The character of the total power operation, with Tobias Barthel, Geometry and Topology,
2017 . - Centralizers in good groups are good, with Tobias Barthel, Algebraic and Geometric Topology,
2016 . - On the ring of cooperations for 2-primary connective topological modular forms, with Mark Behrens, Kyle Ormsby, and Vesna Stojanoska, accepted by Journal of Topology
. - A transchromatic proof of Strickland's theorem, with Tomer M. Schlank, Advances in Mathematics,
2015 . - Rational cohomology from supersymmetric field theories, with Chris Schommer-Pries
. - A relative Lubin-Tate theorem via meromorphic formal geometry, with Aaron Mazel-Gee and Eric Peterson, Algebraic and Geometric Topology,
2015 . - Subgroups of p-divisible groups and centralizers in symmetric groups, Transactions of the AMS,
2015 . - Transchromatic twisted character maps, Journal of Homotopy and Related Structures,
2015 . - Transchromatic generalized character maps, Algebraic and Geometric Topology,
2013 .
Expository and Notes
- An introduction to HKR character theory, Appendix in Formal geometry and bordism operations, Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2018 by Eric Peterson.
- The E-theory Seminar Notes. These are notes from the talks, they were written primarily by Eric Peterson.
Talk Notes
- Notes from a talk on the character of the total power operation.
- Notes from an introductory talk on etale homotopy theory.
Programming
I have contributed code to Macaulay 2. In particular, I wrote the package RationalPoints.m2 and coauthored the packages GenericInitialIdeal.m2, NoetherNormalization.m2, and Regularity.m2. Currently, I am working with an undergraduate lab group at Kentucky to add code to Sage to work with formal group laws. Here is a calculation of the universal formal group law.
Art
In the spring of 2012 I took a print-making class at MIT. Some of my art is below:
People
Here are some of my collaborators:
Tobias Barthel, Mark Behrens, Dan Berwick-Evans, Peter Bonventre, Martin Frankland, Bert Guillou, Aaron Mazel-Gee, Zhen Huan, Niko Naumann, Justin Noel, Kyle Ormsby, Eric Peterson, Sune Precht Reeh, Tomer Schlank, Chris Schommer-Pries, David Spivak, Vesna Stojanoska.