Publications and Preprints


Research Papers:

1.      A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007), 2043-2058.



2.      Three models for the homotopy theory of homotopy theories, Topology 46 (2007), 397-436. 


Longer thesis version (University of Notre Dame, 2005)

3.      Rigidification of algebras over multi-sorted theories, Algebr. Geom. Topol. 6 (2006) 1925-1955.


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.


6.      Adding inverses to diagrams encoding algebraic structures, Homology, Homotopy Appl. 10(2), 2008, 149–174.


and erratum


7.      Complete Segal spaces arising from simplicial categories, Trans. Amer. Math. Soc. 361 (2009), 525-546.


8.       Adding inverses to diagrams II: Invertible homotopy theories are spaces, Homology, Homotopy Appl. 10(2), 2008, 175–193.


and erratum   


9.      Homotopy fiber products of homotopy theories, Israel Journal of Mathematics 185 (2011), 389-411.



10.  Derived Hall algebras for stable homotopy theories, Cah. Topol. Géom. Différ. Catég. 54 (2013), no. 1, 28–55.



11.  Homotopy limits of model categories and more general homotopy theories, Bull. Lond. Math. Soc. 44 (2012), no. 2, 311–322. 



12.  Reedy categories and the θ-construction (with C. Rezk), Math. Z. 274 (1), 2013, 499-514.



13.   Comparison of models for (∞,n)-categories, I (with C. Rezk), Geom. Topol. 17 (2013), no. 4, 2163–2202. 



14.  Reedy categories which encode the notion of category actions (with P. Hackney), Fund. Math.  228 (2015), no. 3, 193–222.



15.  Group actions on Segal operads (with P. Hackney), Israel J. Math. 202 (2014), no. 1, 423–460. 



16.  Homotopy colimits of model categories, An Alpine Expedition through Algebraic Topology, Contemp. Math., 617 (2014), 31-37.



17.  Group actions on Γ-spaces (with P. Hackney), Manifolds and K-Theory, Contemp. Math, 682 (2017) 39-50.



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. 



19.  Classification of problematic subgroups of U(n) (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren), to appear in Trans. Amer. Math. Soc.  



20.  Equivalence of models for equivariant (∞,1)-categories, Glasg. Math. J., 59 (2017), no. 1, 237–253. 



21.  Equivariant complete Segal spaces (with S.G. Chadwick), Homology, Homotopy, and Appl. 17(2), 2015, 371-381. 



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.



The Homotopy Theory of (∞,1)-Categories, Cambridge University Press, 2018.

(By my contract, I can make the pdf available freely 1 year after publication, so a version will be made available here in March 2019.)

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.



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.



3.      Cluster categories for topologists (with M. Robertson), Stacks and Categories in Geometry, Topology and Algebra, Contemp. Math. 643 (2015) 25-35.


Papers written for or with undergraduates:

1.      Groupoid cardinality and Egyptian fractions (with C. Walker), College Math. J. 46 (2015) 122-129.

(older, more formal version)


2.      Action graphs and Catalan numbers (with G. Alvarez and R. Lopez), J. Integer Seq. 18 (2015), Article 15.7.2.


Submitted preprints:

1.      Comparison of models for (∞,n)-categories, II (with C. Rezk)



2.      Action graphs, planar rooted forests, and self-convolutions of the Catalan numbers (with C. Harper, R. Keller, and M. Rosi-Marshall)



Unpublished Notes:

Workshop on the homotopy theory of homotopy theories

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