Publications

On the Unicity of the Homotopy Theory of Higher Categories, Joint with Clark Barwick. accepted for publication, Journal of the AMS.
arXiv:1112.0040

Singular cohomology from supersymmetric field theories, joint with Nathaniel Stapleton. accepted for publication, Advances in Mathematics.
arXiv:1403.1303

Dualizable tensor categories, joint with Christopher Douglas and Noah Snyder. accepted for publication, Memoirs of the AMS.
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

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

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

Coherence for symmetric monoidal bicategories

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

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

The 3-category of Tensor Categories, joint with Christopher Douglas and Noah Snyder.