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, Lukas Brantner, Markus Hausmann, Niko Naumann, Thomas Nikolaus, Justin Noel, Eric Peterson, Sune Precht Reeh, Tomer Schlank, and Chris Schommer-Pries on a variety of projects.

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, Martin Frankland, Bert Guillou, Aaron Mazel-Gee, Justin Noel, Kyle Ormsby, Eric Peterson, Sune Precht Reeh, Tomer Schlank, Chris Schommer-Pries, David Spivak, Vesna Stojanoska.