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Michler Fellow, Visiting Scholar
Homotopy theory, algebraic topology
My research is concerned with the homotopy theory of different kinds of algebraic structures, often themselves taken to be defined up to homotopy. In particular I have compared different approaches to notions of categories up to homotopy, as well as variants such as homotopical higher categories and homotopy operads. Currently, I am interested 2-Segal spaces, which can be thought of as topological category-like structures but for which composition is not always defined. They are particularly interesting because they arise as the output of the Waldhausen construction in algebraic K-theory. I am interested looking at different examples of algebraic K-theory through this lens, as well as investigating algebraic objects such as Hall algebras which can in turn be produced from 2-Segal spaces.
- The Homotopy Theory of (∞,1)-Categories, Cambridge University Press, 2018.
- 2-Segal sets and the Waldhausen construction (with A. Osorno, V. Ozornova, M. Rovelli, and C.I. Scheimbauer), Topology Appl.,235 (2018) 445--484.
- Comparison of models for (∞,n)-categories, I (with C. Rezk), Geom. Topol. 17 (2013), no. 4, 2163–2202.
- Complete Segal spaces arising from simplicial categories, Trans. Amer. Math. Soc. 361 (2009), 525-546.
- Three models for the homotopy theory of homotopy theories, Topology 46 (2007), 397-436.
- A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007), 2043-2058.