Paul VanKoughnett
I'm a Golomb Visiting Assistant Professor at Purdue. Next fall, I'll be a visiting assistant professor at Texas A&M University. I work on the intersection of stable homotopy theory and number theory.
MATH 842
Department of Mathematics, Purdue University
150 N. University St.
Evanston, IL 60201
pvankoug AT purdue DOT edu
My CV.
Research

I study chromatic stable homotopy theory from the point of view of the geometry of formal groups and p-divisible groups. I'm particularly interested in transchromatic questions: what happens when formal groups change height, and what this tells us about chromatic localizations. I'm also interested in using the analytic geometry of Lubin-Tate space to study the action of the Morava stabilizer group.

I made a short video summary of my current research for the electronic Algebraic Topology Employment Network. You can watch it on Youtube.

Dominic Leon Culver and Paul VanKoughnett, On the K(1)-local homotopy of tmf∧tmf (2019), arXiv:1908.01904.

Piotr Pstrągowski and Paul VanKoughnett, Abstract Goerss-Hopkins-Theory (2019), submitted, arXiv:1904.08881.

My thesis: Localizations of E-theory and Transchromatic Phenomena in Stable Homotopy Theory.

Other notes, expository writing, and seminars

In spring 2021, I am running a learning seminar on stable homotopy theory and spectra.

Unfinished notes on topological automorphic forms, April 2014.

Notes for Paul Goerss's fall 2014 class on the Sullivan conjecture.

Notes and references for the fall 2013 topological automorphic forms seminar.

Talbots: structured ring spectra 2017, motivic homotopy theory 2014, chromatic homotopy theory 2013 (for which I typed up a whole lot of notes).

Talk notes

Introduction to infinity-categories, a student seminar, October 2016.

Stable infinity-categories, Northwestern pre-Talbot seminar, February 2016.

The Steenrod algebra, a student algebraic topology seminar, January 2016.

Stable homotopy theory and geometry, Northwestern graduate student seminar, October 2014.

K3 cohomology theories, K3 seminar, September 2014.

Talk for number theorists on TMF, Northwestern number theory day, September 2014.

The Kervaire invariant, more focused on geometric topology aspects (and the construction of the Kervaire manifold) than stable homotopy theory, Kan seminar, May 2014.

Representability of algebraic K-theory by a motivic spectrum, Talbot, March 2014.

p-divisible groups, topological automorphic forms seminar, October 2013.

Kuhn's proof of the splitting of Goodwillie towers after finite K(n)-localization, summer Goodwillie calculus seminar, August 2013.

The construction of the A-hat genus, viewed as a height-1 analogue of the Ando-Hopkins-Rezk string orientation of tmf, reading course on Thom spectra, May 2013.

Introduction to spectra and Bousfield localization, Northwestern pre-Talbot seminar, January 2013.

Teaching

In spring 2020, fall 2020, and spring 2021, I taught Math 351: Elementary Linear Algebra. (Current students can find information about the class on the Blackboard page.)

In fall 2019, I taught Math 303: Differential Equations and Partial Differential Equations for Engineering and the Sciences.

In fall 2018, I taught Math 266: Ordinary Differential Equations. I also supervised an undergraduate reading course on simplicial methods in homotopy theory.