Publications and Preprints



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. 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.

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


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

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


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



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



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



13. 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.



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

      (older, more formal version)        


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



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



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



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



19. Homotopy colimits of model categories, An alpine expedition through algebraic topology, Contemp. Math., 617 (2014), 31-37.



20. Group actions on Γ-spaces (with P. Hackney), to appear in Goodwillie conference proceedings



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



22. 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.   



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



24. Classification of problematic subgroups of U(n) (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren)



25. Equivalence of models for equivariant (∞,1)-categories, to appear in Glasgow Mathematical Journal.



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



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



28. 2-Segal sets and the Waldhausen construction (with A. Osorno, V. Ozornova, M. Rovelli, and C.I. Scheimbauer)



Unpublished Notes:


Workshop on the homotopy theory of homotopy theories

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