Publications and Preprints
1. A model category structure on the category
of simplicial categories, Trans. Amer. Math. Soc. 359 (2007),
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.
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.
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.
10. Homotopy fiber products of homotopy theories, Israel Journal of Mathematics 185 (2011), 389-411.
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), to appear in College Mathematics Journal.
15. Reedy categories and the θ-construction (with C. Rezk), Math. Z. 274 (1), 2013, 499-514.
17. Reedy categories which encode the notion of category actions (with P. Hackney), to appear in Fundamenta Mathematicae
18. Group actions on Segal operads (with P. Hackney), to appear in Israel Journal of Mathematics.
19. Homotopy colimits of model categories, to appear in Arolla proceedings.
20. Group actions on Γ-spaces (with P. Hackney)
21. Cluster categories for topologists (with M. Robertson), to appear in CATS4 proceedings
22. Fixed points of p-toral groups acting on partition complexes (with R. Joachimi, K. Lesh, V. Stojanoska, and K. Wickelgren), to appear in Women in Topology proceedings
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)
26. Equivariant complete Segal spaces (with S.G. Chadwick)
27. Action graphs and Catalan numbers (with G. Alvarez and R. Lopez)
http://www.math.ucr.edu/~jbergner/papers.html Last modified: 3 March 2015