Curriculum Vitae
This CV is an outline of my professional activity. You can also download a pdf version of my CV.
Curriculum Vitae Niles Johnson
Newark Campus
Department of Mathematics
The Ohio State University
[email protected]
nilesjohnson.net
__________________________________________________________________________
Employment
Professor
2024
–
present
Department of Mathematics, The Ohio State University, Newark
Associate Professor
2018
–
2024
Department of Mathematics, The Ohio State University, Newark
Assistant Professor
2012
–
2018
Department of Mathematics, The Ohio State University, Newark
VIGRE Postdoctoral Associate
2009
–
2012
Department of Mathematics, University of Georgia
Education
University of Chicago, IL
2003
–
2009
Ph.D. in Mathematics, August 2009
M.S. in Mathematics, May 2005
M.S. in Mathematics, May 2005
University of Rochester, NY
1999
–
2003
B.A., M.A., majoring in Mathematics, May 2003
Books
Homotopy Theory of Enriched Mackey Functors
Joint with Donald Yau. LMS Lecture Note Series, Volume 492. Cambridge University Press, 2025.
ISBN: 9781009519564.
Bimonoidal Categories, En-Monoidal Categories, and Algebraic
K-Theory, Volume III: From Categories to Structured Ring
Spectra
Joint with Donald Yau. Mathematical Surveys and Monographs, Volume 285. American
Mathematical Society, 2024. ISBN: 9781470478117. AMS bundle of all three volumes. Preprint
version of all three volumes.
2-Dimensional Categories
Research Articles
Invertibility and Parity in Symmetric Monoidal Categories
Joint with Nick Gurski. Applied Categorical Structures.
Collection honouring Robert Paré for his 80th birthday (2026), Article 34, pp 1–41.
Collection honouring Robert Paré for his 80th birthday (2026), Article 34, pp 1–41.
Universal pseudomorphisms, with applications to diagrammatic
coherence for braided and symmetric monoidal functors
The symmetric monoidal 2-category of permutative categories
Multicategories Model All Connective Spectra
Multifunctorial K-Theory is an Equivalence of Homotopy
Theories
Homotopy Equivalent Algebraic Structures in Multicategories
and Permutative Categories
Multifunctorial Inverse K-Theory
2-categorical opfibrations, Quillen’s Theorem B, and S−1S
Joint with Nick Gurski and Angélica Osorno. New York Journal of Mathematics.
Vol. 27 (2021), pp 1009–1059.
Vol. 27 (2021), pp 1009–1059.
The 2-dimensional stable homotopy hypothesis
Joint with Nick Gurski and Angélica Osorno. Journal of Pure and Applied Algebra.
Vol. 223 (2019) No. 10 , pp 4348–4383.
Vol. 223 (2019) No. 10 , pp 4348–4383.
K-theory for 2-categories
Stable Postnikov data of Picard 2-categories
Joint with Nick Gurski, Angélica Osorno, and Marc Stephan. Algebraic & Geometric
Topology.
Vol. 17 (2017) Iss. 5, pp 2763–2806.
Vol. 17 (2017) Iss. 5, pp 2763–2806.
Extending homotopy theories across adjunctions
Joint with Nick Gurski and Angélica Osorno. Homology, Homotopy and Applications.
Vol. 19 (2017), No. 2, pp 89–110.
Vol. 19 (2017), No. 2, pp 89–110.
Lifting homotopy T-algebra maps to strict maps
Azumaya Objects in Triangulated Bicategories
First cohomology for finite groups of Lie type: simple modules
with small dominant weights
Joint with UGA VIGRE Algebra Group. Transactions of the American Mathematical
Society.
Vol. 365 (2013) No. 2, pp 1025–1050.
Vol. 365 (2013) No. 2, pp 1025–1050.
Modeling stable one-types
Joint with Angélica Osorno. Theory and Applications of Categories.
Vol. 26 No. 20 (2012), pp 520–537.
Vol. 26 No. 20 (2012), pp 520–537.
Second cohomology for finite groups of Lie type
For complex orientations preserving power operations,
p-typicality is atypical
Expository Articles
Calculating complex cosine clusters
2022
Topological Invariants from Higher Categories
2019
Joint with Nick Gurski and Angélica Osorno. Notices of the Americal Mathmatical Society, Vol. 66
(2019) No. 8, pp. 1225–1237
Computer Software
Visualization of A(2)
February
2013
Joint with Robert Bruner. Interactive javascript application for visualizing multiplicative structure of
Steenrod subalgebra.
Available at https://nilesjohnson.net/Aof2/.
Available at https://nilesjohnson.net/Aof2/.
Multivariate Power series Arithmetic
August
2011
Sage software peer-reviewed and included since version 4.7.1
Composition factors of Weyl modules
July
2011
Sage software for computing composition factors of certain Weyl modules.
Available at https://nilesjohnson.net/rep-thy.html.
Available at https://nilesjohnson.net/rep-thy.html.
Invited Talks 2022–present
Algebra morphism coherence
Quantum Symmetries Group Seminar, Ohio State University
April
2024
Graded Picard categories and the 2-type of the sphere
Topology Seminar, University of Haifa
April
2022
Algebra Seminar, Florida State University
March
2022
Algebraic K-theory for 2-categories
Colloquium, Florida State University
March
2022
Animations
Hopf fibration – fibers and base
August
2011
Visualizing Seven-Manifolds
January
2012
https://nilesjohnson.net/seven-manifolds
Gives a visualization of exotic seven-spheres and related manifolds.
Presented at the Second Abel Conference in celebration of John Milnor.
Gives a visualization of exotic seven-spheres and related manifolds.
Presented at the Second Abel Conference in celebration of John Milnor.
Teaching 2022–Present
Calculus
2020,
2023–2025
Ohio State University, Newark
Calculus II
2023–2024
Ohio State University, Newark
College Algebra
2021–2022
Ohio State University, Newark
Ph.D. Students
Amogh Parab
Graduated
2026
Michael Horst
Graduated
2020
Corey Staten
Graduated
2018
Service 2022–Present
Site Administrator, MathMeetings.net
2010–present
Conference announcement and listings
Managing Editor, Homology, Homotopy and Applications
2026–present
International Press of Boston
Member, Academic Standards Committee
2025–present
Ohio State University, Newark Campus
Faculty Representative
2024–2025
Ohio State University, Newark Campus
Past-Chair, Faculty Assembly
2022–2023
Ohio State University, Newark Campus
Chair, Faculty Assembly
2021–2022
Ohio State University, Newark Campus
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