F.L. Griffin Associate Professor of Mathematics
Department of Mathematics and Statistics
Reed College
Office: L305
Email: aosorno at reed dot edu
Andrew Blumberg, Mike Hill, Kyle Ormsby, Constanze Roitzheim and I wrote an article for Notices of the AMS introducing homotopical combinatorics.
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.
Teaching
Fall 2024: MATH 201 - Linear Algebra
Fall 2024: MATH 412 - Topics in Algebra: Galois Theory
Uniquely compatible transfer systems for cyclic groups of order prqs
(with Kristen Mazur, Constanze Roitzheim, Rekha Santhanam, Danika Van Niel and Valentina Zapata Castro) PDF
Equivariant infinite loop space theory, I. The space level story
(with J. Peter May and Mona Merling) PDF
Research publications:
The symmetric monoidal 2-category of permutative categories
(with Nick Gurski and Niles Johnson). High. Struct. 8, no. 1, 244-320, 2024. PDF
Model structures on finite total orders
(with Scott Balchin, Kyle Ormsby, and Constanze Roitzheim). Math. Z. 304, no. 3, Paper No. 40, 35 pp, 2023. PDF
Multiplicative equivariant K-theory and the Barratt-Priddy-Quillen theorem
(with Bert Guillou, J. Peter May, and Mona Merling). Adv. Math. 414, Paper No. 108865, 111 pp, 2023. PDF
Saturated and linear isometric transfer systems for cyclic groups of order p
mqn
(with Usman Hafeez, Peter Marcus, and Kyle Ormsby)
Topology Appl., 317, Paper No. 108162, 20 pp., 2022. PDF.
Self-duality of the lattice of transfer systems via weak factorization systems
(with Evan Franchere, Kyle Ormsby, Weihang Qin, and Riley Waugh). Homology Homotopy Appl. 24, no. 2, 115-134, 2022. PDF
2-categorical opfibrations, Quillen's Theorem B, and S-1S
(with Nick Gurski and Niles Johnson). New York J. Math. 27, 1009-1059, 2021. PDF
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). Ann. K-Theory 6, no. 1, 97-136, 2021. 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). Algebr. Geom. Topol. 21, no. 3, 1267-1326, 2021. 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:
Homotopical Combonatorics
(joint with Andrew Blumberg, Mike Hill, Kyle Ormsby, and Constanze Roitzheim.) Notices of the AMS, Vol 71, No 2, 2024. PDF
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.
