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]
https://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
August
2012
–
2018
Department of Mathematics, The Ohio State University, Newark
VIGRE Postdoctoral Associate
August
2009
–
May
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
Honors and Awards
Scholarly Accomplishment Award
March
2018
Newark Campus, Tenure-track category.
Teaching Excellence Award
March
2016
Newark Campus, Tenure-track category.
Service Award
March
2016
Newark Campus, Tenure-track category.
Books
Homotopy Theory of Enriched Mackey Functors
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
Universal pseudomorphisms, with applications to diagrammatic
coherence for braided and symmetric monoidal functors
Joint with Nick Gurski. Submitted.
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 2016–present
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
Colloquium, University of Louisiana, Lafayette
February
2021
Topology Seminar, University of Chicago
March
2020
Colloquium, Case Western Reserve University
November
2019
Visualizing the Hopf fibration
Colloquium, Reed College
October
2020
Homotopy theory of Picard categories
Topology Seminar, Case Western Reserve University
November
2019
The algebra of stable 2-types
Topology Seminar, Johns Hopkins University
February
2019
A 2-categorical group-completion
Topology Seminar, University of Kentucky
February
2019
The 2-dimensional stable homotopy hypothesis
AMS Spring Sectional Meeting, Vanderbilt University
April
2018
A 2-categorical group completion
Special Session on Homotopy Theory, AMS Spring Central Sectional
Meeting, Indiana University
April
2017
Categorical models in homotopy theory
Topology Seminar, University of Kentucky
March
2017
Algebraic models of stable Postnikov invariants
Workshop on “Operations in Highly Structured Homology Theories”
Banff International Research Station
Banff International Research Station
May
2016
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 2016–Present
Calculus
2020,
2023
Ohio State University, Newark
Calculus II
2023
Ohio State University, Newark
College Algebra
2021–2022
Ohio State University, Newark
Calculus and its History for Teachers
2016,
2018
Ohio State University, Newark
Algebra and Coordinate Geometry for Teachers
2015,
2017,
2019
Ohio State University, Newark
Measurement and Geometry for Teachers
2014
–
2019
Ohio State University, Newark
Number and Operations for Teachers
2014
–
2018
Ohio State University, Newark
Ph.D. Students
Amogh Parab
2020–present
Michael Horst
Graduated
2020
Corey Staten
Graduated
2018
Service 2016–Present
Site Administrator, MathMeetings.net
2010
–
present
Past-Chair, Faculty Assembly
2022
–
2023
Ohio State University, Newark Campus
Chair, Faculty Assembly
2021
–
2022
Ohio State University, Newark Campus
Vice-Chair, Faculty Assembly
2020
–
2021
Ohio State University, Newark Campus
Academic Affairs Committee
2017
–
2019
Oho State University, Newark campus
Presenter, Mrs. Gordon’s 2nd grade class
December
09,
2022
“Snowflake Symmetry”
Garfield Elementary School
Garfield Elementary School
Presenter, Math Collaboration Group
February
20,
2022
“Euler Characteristic: An introduction to algebraic topology”
Ohio High School Students
Ohio High School Students
Organizer, Mayday 2019 Conference
October
4
–
6
2019
University of Chicago; https://nilesjohnson.net/mayday2019/
Presenter, Teaching and Learning Seminar
February
28,
2019
“Constructing mathematical knowledge for elementary educators”
University of Kentucky
University of Kentucky
Presenter, Blowing Off STEAM
January
9,
2018
“Confessions of a Mathematician”
Thirty One West
Thirty One West
Presenter, Franklinton Friday
December
8,
2017
“Snowflake Symmetry”
OSU STEAM Factory
OSU STEAM Factory
Presenter, Ms. Cline’s 2nd grade class
December
15,
2017
“Snowflake Symmetry”
Garfield Elementary School
Garfield Elementary School
Secretary, Faculty Assembly
2015
–
2016
Ohio State University, Newark campus
Panelist, AWM Panel Discussion
August
2016
“Prioritizing Your Career and Professional Goals”
Mathfest, Columbus OH
Mathfest, Columbus OH
Organizer, Spring 2016 Midwest Topology Seminar
May
14,
2016
Organizer, 2016 Pi Measurement Challenge
March
13,
2016
Presenter, Chamber of Commerce After Hours
February
18,
2016
Ohio State University, Newark campus
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