Publications

On the Unicity of the Homotopy Theory of Higher Categories, Joint with Clark Barwick. Journal of the AMS, 34 (2021), no. 4, 1011-1058.
arXiv:1112.0040

Singular cohomology from supersymmetric field theories, joint with Nathaniel Stapleton. Advances in Mathematics, 390 (2021), Paper No. 107944.
arXiv:1403.1303

Dualizable tensor categories, joint with Christopher Douglas and Noah Snyder. Memoirs of the AMS, 268 (2020), no. 1308.
arXiv:1312.7188

The balanced tensor product of module categories, joint with Christopher Douglas and Noah Snyder. Kyoto Journal of Mathematics, Vol 59, Number 1 (2019), 167-179
arXiv:1406.4204

Tori Detect Invertibility of Topological Field Theories, Geometry & Topology 22 (2018) 2713-2756.
arXiv:1511.01772

Dualizability in Low-Dimensional Higher Category Theory, Topology and Field Theories, Contemp. Math. , vol. 613, Amer. Math. Soc., Providence, RI, 2014. arXiv:1308.3574

Central extensions of smooth 2–groups and a finite-dimensional string 2–group, Geometry & Topology 15 (2011) 609–676.
arXiv:0911.2483

Ph.D. Dissertation. The Classification of Two-Dimensional Extended Topological Field Theories. (208 pages, 107 figures, with an index).
arXiv:1112.1000 (more recent version, 7 Dec, 2011)

Examples of Cayley 4-Manifolds, Joint with Weiqing Gu. Houston Journal of Mathematics 30 (2004), no. 1, 55–87.

Preprints

Semisimple Field Theories Detect Stable Diffeomorphism, joint with David Reutter. arXiv:2206.10031

Invertible Topological Field Theories. arXiv:1712.08029

Modular categories as representations of the 3-dimensional bordism 2- category, joint with Bruce Bartlett, Christopher Douglas, and Jamie Vicary.
arXiv:1509.06811

Extended 3-dimensional bordism as the theory of modular objects, joint with Bruce Bartlett, Christopher Douglas, and Jamie Vicary.
arXiv:1411.0945

In preparation

Higher Categories via higher A-infinity Operads, joint with Nate Bottman an dViktoriya Ozornova.

The Relative Tangle Hypothesis

A finite presentation of the oriented 3-dimensional bordism bicategory, joint with Bruce Bartlett, Christopher Douglas, and Jamie Vicary.

Dualizable tensor categories II: Homotopy SO(3)-actions, joint with C. Douglas and N. Snyder.

Twisted cohomology via twisted field theories, joint with Stephan Stolz and Peter Teichner.

On Waldhausen’s Splitting of A-theory.

Coherence for symmetric monoidal bicategories

Extensions of symmetric monoidal bicategories, joint with Bruce Bartlett, Christopher Douglas, and Jamie Vicary.