Associate Professor
Department of Mathematics
Reed College
Office: L305
Email: aosorno at reed dot edu
I am on sabbatical during the 2020-2021 academic year.
Nick Gurski, Niles Johnson and I wrote an article for Notices of the AMS outlining our research on the stable homotopy hypothesis.
I do research in algebraic topology. I am particularly interested in higher category theory and its connections with higher K-theory. In 2010, I got my PhD at MIT with Mark Behrens. From 2010 to 2013, I was a postdoc at the University of Chicago working with Peter May.
Equivariant infinite loop space theory, I. The space level story.
(with J. Peter May and Mona Merling). PDF.
2-categorical opfibrations, Quillen's Theorem B, and S^{-1}S.
(with Nick Gurski and Niles Johnson). PDF.
Self-duality of the lattice of transfer systems via weak factorization systems.
(with Evan Franchere, Kyle Ormsby, Weihang Qin, and Riley Waugh). PDF.
Multiplicative equivariant K-theory and the Barratt-Priddy-Quillen theorem.
(with Bert Guillou, J. Peter May, and Mona Merling). PDF.
Research publications:
Biased permutative equivariant categories
(with Kayleigh Bangs, Skye Binegar, Young Kim, Kyle Ormsby, David Tamas-Parris, Livia Xu). Homology Homotopy Appl. 23, no.
1, 77-100, 2021. PDF
Comparison of Waldhausen constructions.
(with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer). To appear in Ann. K-theory. PDF
A multiplicative comparison of Waldhausen and Segal K-theory
(with Anna Marie Bohmann). Math. Z. 295, no. 3-4, 1205-1243, 2020. PDF
2-Segal objects and the Waldhausen construction
(with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer). To appear in Algebr. Geom. Topol. PDF
Symmetric monoidal G-categories and their strictification
(with Bert Guillou, J. Peter May and Mona Merling). Q. J. Math. 71, no. 1, 207-246, 2020. PDF.
The edgewise subdivision criterion for 2-Segal objects
(with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer). Proc. Amer. Math. Soc. 148, no. 1, 71-82, 2020. PDF
The 2-dimensional stable homotopy hypothesis
(with Nick Gurski and Niles Johnson). J. Pure Appl. Algebra 223(10):4348-4383, 2019. PDF.
A symmetric monoidal and equivariant Segal infinite loop space machine
(with Bert Guillou, J. Peter May and Mona Merling). J. Pure Appl. Algebra 223(6):2425-2454, 2019. PDF.
2-Segal sets and the Waldhausen construction
(with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer). Topology Appl. 235, 445-484, 2018. PDF
Stable Postnikov data of Picard 2-categories
(with Nick Gurski, Niles Johnson and Marc Stephan). Algebr. Geom. Topol. no. 5, 2763-2806, 2017. PDF
Extending homotopy theories across adjunctions
(with Nick Gurski and Niles Johnson). Homology Homotopy Appl. 19 no. 2, 89-110, 2017. PDF
K-theory for 2-categories
(with Nick Gurski and Niles Johnson). Adv. Math. 322: 378-472, 2017. PDF
Constructing equivariant spectra via categorical Mackey functors
(with Anna Marie Bohmann). Algebr. Geom. Topol. 15(1):537-563, 2015. PDF
A model structure on GCat
(with Anna Marie Bohmann, Kristen Mazur, Viktoriya Ozornova, Kate Ponto and Carolyn Yarnall). Women in Topology: Collaborations in Homotopy Theory, Contemp. Math. 641, 123-134, 2015. PDF
Infinite loop spaces, and coherence for symmetric monoidal bicategories
(with Nick Gurski). Adv. Math. 246:1-32, 2013. PDF
Modeling stable one-types
(with Niles Johnson). Theory Appl. Categ. 26:520-537, 2012. PDF
Spectra associated to symmetric monoidal bicategories. Algebr. Geom. Topol. 12(1):307-342, 2012. PDF
Explicit formulas for 2-characters. Topology Appl., 157(2):369-377, 2010. PDF
Other publications:
Topological Invariants of Higher Categories
(joint with Nick Gurski and Niles Johnson.) Notices of the AMS, Vol 66, No 8, 2019. PDF
Invitación a la teoría de homotopía: Grupo
fundamental y espacios recubridores (Introduction to basic concepts in homotopy theory - in Spanish). Lect. Mat. 39(1):29-48, 2018. PDF
Espacios de lazos infinitos (Survey paper about infinite loop spaces - in Spanish). Bol. Mat. 18(2):163-182, 2011. PDF
I am the administrator for the mailing list of the Cascade Topology Seminar. If you would like to be added to the list, please send me an email with your request.
I was the chair of the scientific committee for the Topology Ecuador 2017 Conference that took place in the Galápagos Islands, Ecuador, in August 14-18, 2017.