Research Papers:
1. A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007), 2043-2058.
(math.AT/0406507)
2. Three models for the homotopy theory of homotopy theories, Topology 46 (2007), 397-436.
(math.AT/0504334)
Longer thesis version (University of Notre Dame, 2005)
3. Rigidification of algebras over multi-sorted theories, Algebr. Geom. Topol. 6 (2006) 1925-1955.
(math.AT/0508152)
4. Simplicial monoids and Segal categories, Contemp. Math. 431 (2007) 59-83.
and correction
(math.AT/0508416; math.AT/0806.1767)
5. A characterization of fibrant Segal categories, Proc. Amer. Math. Soc. 135 (2007) 4031 4037.
(math.AT/0603400)
6. Adding inverses to diagrams encoding algebraic structures, Homology, Homotopy Appl. 10(2), 2008, 149–174.
(math.AT/0610291)
and erratum
7. Complete Segal spaces arising from simplicial categories, Trans. Amer. Math. Soc. 361 (2009), 525-546.
(math.AT/0704.1624)
8. Adding inverses to diagrams II: Invertible homotopy theories are spaces, Homology, Homotopy Appl. 10(2), 2008, 175–193.
(math.AT/0710.2254)
and erratum
9. Homotopy fiber products of homotopy theories, Israel Journal of Mathematics 185 (2011), 389-411.
(math.AT/0811.3175)
10. Derived Hall algebras for stable homotopy theories, Cah. Topol. Géom. Différ. Catég. 54 (2013), no. 1, 28–55.
(math.AT/0910.1861)
11. Homotopy limits of model categories and more general homotopy theories, Bull. Lond. Math. Soc. 44 (2012), no. 2, 311–322.
(math.AT/1010.0717)
12. Reedy categories and the θ-construction (with C. Rezk), Math. Z. 274 (1), 2013, 499-514.
(math.AT/1110.1066)
13. Comparison of models for (∞,n)-categories, I (with C. Rezk), Geom. Topol. 17 (2013), no. 4, 2163–2202.
(math.AT/1204.2013)
14. Reedy categories which encode the notion of category actions (with P. Hackney), Fund. Math. 228 (2015), no. 3, 193–222.
(math.AT/1207.3467)
15. Group actions on Segal operads (with P. Hackney), Israel J. Math. 202 (2014), no. 1, 423–460.
(math.AT/1207.3465)
16. Homotopy colimits of model categories, An Alpine Expedition through Algebraic Topology, Contemp. Math., 617 (2014), 31-37.
(math.AT/1212.4541)
17. Group actions on Γ-spaces (with P. Hackney), Manifolds and K-Theory, Contemp. Math, 682 (2017) 39-50.
(math.AT/1212.4542)
18. Fixed points of p-toral groups acting on partition complexes (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren), Women in Topology: Collaborations in Homotopy Theory, Contemp. Math. 641 (2015), 83-96.
(math.AT/1401.0491)
19. Classification of problematic subgroups of U(n) (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren), Trans. Amer. Math. Soc. 371 (2019) 6739-6777.
(math.AT/1407.0062)
20. Equivalence of models for equivariant (∞,1)-categories, Glasg. Math. J., 59 (2017), no. 1, 237–253.
(math.AT/1408.0038)
21. Equivariant complete Segal spaces (with S.G. Chadwick), Homology, Homotopy, and Appl. 17(2), 2015, 371-381.
(math.AT/1502.06637)
22. 2-Segal sets and the Waldhausen construction (with A. Osorno, V. Ozornova, M. Rovelli, and C.I. Scheimbauer), Topology Appl.,235 (2018) 445--484.
(math.AT/1609.02853)
23. The edgewise subdivision criterion for 2-Segal objects (with A. Osorno, V. Ozornova, M. Rovelli, and C. Scheimbauer), to appear in Proc. Amer. Math. Soc. 148 (2020) 71-82.
(math.AT/1807.05069)
24. 2-Segal objects and the Waldhausen construction (with A. Osorno, V. Ozornova, M. Rovelli, and C. Scheimbauer), to appear in Alg. Geom. Topol.
(math.AT/1809.10924)
25. Comparison of models for (∞,n)-categories, II (with C. Rezk), to appear in J. Topol.
(math.AT/1406.4182)
25. Comparison of Waldhausen constructions (with A. Osorno, V. Ozornova, M. Rovelli, and C. Scheimbauer), to appear in Ann. K-Theory.
(math.AT/1901.03606)
Book:
The Homotopy Theory of (∞,1)-Categories, Cambridge University Press, 2018.
Expository Papers:
1. A survey of (∞,1)-categories, in J. Baez and J. P. May, Towards Higher Categories, IMA Volumes in Mathematics and Its Applications, Springer, 2010, 69-83.
(math.AT/0610239)
2. Models for (∞, n)-categories and the cobordism hypothesis, in H. Sati and U. Schreiber, ed., Mathematical Foundations of Quantum Field Theory and Perturbative String Theory, Proc. Sympos. Pure Math. 83 (2011) 17-30.
(math.AT/1011.0110)
3. Cluster categories for topologists (with M. Robertson), Stacks and Categories in Geometry, Topology and Algebra, Contemp. Math. 643 (2015) 25-35.
(math.AT/1308.2560)
4. A survey of models for (∞,n)-categories, in Handbook of Homotopy Theory (Haynes Miller, ed,), CRC Press, 2020, 263-295.
(math.AT/1810.10052)
5. Modeling homotopy theories, Notices Amer. Math. Soc. 66 (2019) 1423-1432.
Papers written for or with undergraduates:
1. Groupoid cardinality and Egyptian fractions (with C. Walker), College Math. J. 46 (2015) 122-129.
2. Action graphs and Catalan numbers (with G. Alvarez and R. Lopez), J. Integer Seq. 18 (2015), Article 15.7.2.
(math.CO/1503.00044)
3. Action graphs, planar rooted forests, and self-convolutions of the Catalan numbers (with C. Harper, R. Keller, and M. Rosi-Marshall)
(math.CO/1807.03005)
Non-technical papers:
1. Writing papers in the mathematical sciences, Academe: First Forays into Academic Writing, Vol. 2, No. 1 (January 2020).
2. What do I do when my paper or grant proposal is rejected?, Notices Amer. Math. Soc. 67 No. 3 (2020) 364—365.
Submitted preprints:
1. Enriched functor categories for functor calculus (with L. Bandklayder, R. Griffiths, B. Johnson, and R. Santhanam)
(math.AT/2003.00071)
Unpublished Notes:
Workshop on the homotopy theory of homotopy theories