My general research interest is in algebraic topology, and my work is broadly motivated by the study of manifolds and cell complexes by algebraic techniques. I have recently been focusing on topological Hochschild homology, algebraic K-theory, transfers, and stable homotopy theory. There is also an emerging connection between my work and homotopy-invariant properties of topological dynamical systems. See my research statement for more information.

In the fall of 2017 I will be starting an assistant professor position at SUNY Binghamton. During the calendar year of 2018 I will be on leave at the Max Planck Institute in Bonn.

We are in the process of organizing a regional topology seminar for the fall of 2017. In the past I organized the Topology Seminar at UIUC and the Stanford student topology seminar, and was involved with the "xkcd" discussion group, and the String topology seminar. I completed my thesis under the direction of Ralph Cohen at Stanford University.

- The Morita equivalence between parametrized spectra and module spectra. (with John Lind; submitted)
- Equivariant A-theory. (with Mona Merling; submitted)
- The transfer map of free loop spaces. (with John Lind; submitted)
- The transfer is functorial. (with John Klein; submitted)
- Cyclotomic structure in the topological Hochschild homology of DX. (Algebraic & Geometric Topology 2017)
- The topological cyclic homology of the dual circle. (Journal of Pure and Applied Algebra 2017)
- Coassembly and the K-theory of finite groups. (Advances in Mathematics 2017)
- A tower connecting gauge groups to string topology. (Journal of Topology 2015)

Other publications:

- The user's guide project: giving experiential context to research papers.

(with Mona Merling, David White, Luke Wolcott, and Carolyn Yarnall; Journal of Humanistic Mathematics) - Duality and linear approximations in Hochschild homology, K-theory, and string topology. (Ph.D. thesis)

In preparation:

- Comparing the norm and Bokstedt models of THH. (with Emanuele Dotto, Irakli Patchkoria, Steffen Sagave, and Calvin Woo)
- Periodic orbits and topological restriction homology. (with Kate Ponto)

There are also errata for my Ph.D. thesis.

In the fall of 2017 I will be teaching linear algebra and graduate topology.

Together with Jenya Sapir I am overseeing a project to create interactive games that teach core intuitions behind linear algebra. You can play the latest prototype here. Last spring this project was part of the Illinois Geometry Lab.

In graduate school I received Stanford's Centennial Teaching Assistant Award. I was also the department liaison for the Center for Teaching and Learning (CTL).

- The Reidemeister trace (free loop transfer) in pictures (JMM 2017)
- A visual introduction to cyclic sets and cyclotomic spectra (YTM 2015)

- A user's guide: Coassembly and the K-theory of finite groups (2015)
- The stable homotopy category (an introduction to spectra, 2012-2014)
- The Steenrod algebra (2012)
- The bar construction and BG (2011)
- Unoriented cobordism and MO (2011)

In preparation:

- A geometric introduction to stable homotopy theory.
- An overview of duality theory and Morita theory.
- The homotopy theory of diagrams, an elementary introduction.
- A user's guide to orthogonal G-spectra.

- Semistability, The Bokstedt smash product, and classical fibrant replacement for diagram spectra (2017)
- Finite spectra (2015)
- Pushouts in the homotopy category do not exist (2014)
- Fibration sequences and pullback squares (2014)
- Fixed points and colimits (2014)
- Homotopy colimits via the bar construction (2014)
- Finiteness, phantom maps, completion, and the Segal conjecture (2013)
- The gluing lemma is left-properness (2013)
- Some facts about QX (2011)