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

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Employment

 
Associate Professor
2018 present

Department of Mathematics, The Ohio State University, Newark
Assistant Professor
August 2012 2018

Department of Mathematics, The Ohio State University, Newark
Postdoctoral Associate in Mathematical Ecology
May 2012 August 2012

Odum School of Ecology, University of Georgia
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
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

 
Bimonoidal Categories, En-Monoidal Categories, and Algebraic K-Theory

Joint with Donald Yau. Submitted.
2-Dimensional Categories

 

Research Articles

 
Multifunctorial K-Theory is an Equivalence of Homotopy Theories

Joint with Donald Yau. To appear in Journal of Homotopy and Related Structures.
Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories

Joint with Donald Yau. Theory and Applications of Categories.
Vol. 38, 2022, No. 30, pp 1156-1208.
Multicategories Model All Connective Spectra

Joint with Donald Yau. To appear in Homology, Homotopy and Applications.
Multifunctorial Inverse K-Theory

Joint with Donald Yau. To appear in Annals of K-Theory.
2-categorical opfibrations, Quillen’s Theorem B, and S1S

Joint with Nick Gurski and Angélica Osorno. New York Journal of Mathematics.
27 (2021), pp 1009–1059.
The 2-dimensional stable homotopy hypothesis

Joint with Nick Gurski and Angélica Osorno. Journal of Pure and Applied Algebra.
223 no. 10 (2019), pp 4348–4383.
Stable Postnikov data of Picard 2-categories

Joint with Nick Gurski, Angélica Osorno, and Marc Stephan. Algebraic & Geometric Topology.
17-5 (2017), pp 2763–2806.
Extending homotopy theories across adjunctions

Joint with Nick Gurski and Angélica Osorno. Homology, Homotopy and Applications.
19 (2017), no. 2, pp 89–110.
K-theory for 2-categories

Joint with Nick Gurski and Angélica Osorno. Advances in Mathematics.
322 (2017), pp 378–472.
Lifting homotopy T-algebra maps to strict maps

Joint with Justin Noel. Advances in Mathematics.
264 (2014), pp 593–645.
Modeling stable one-types

Joint with Angélica Osorno. Theory and Applications of Categories.
26 No. 20 (2012), pp 520–537.
Second cohomology for finite groups of Lie type

Joint with UGA VIGRE Algebra Group. Journal of Algebra.
360 (2012), pp 21–52.
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.
365 No. 2 (2013), pp 1025–1050.
Azumaya Objects in Triangulated Bicategories

Journal of Homotopy and Related Structures.
9 No. 2 (2014), pp 465–493.
For Complex Orientations Preserving Power Operations, p-typicality is Atypical

Joint with Justin Noel. Topology and its Applications.
157 (2010) pp 2271–2288.
 

Expository Articles

 
Topological Invariants from Higher Categories
September 2019

Joint with Nick Gurski and Angélica Osorno. Notices of the Americal Mathmatical Society, vol. 66 no. 8, (2019), 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/.
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.
 

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
May 2016
 

Animations

 
Hopf fibration – fibers and base
August 2011

https://nilesjohnson.net/hopf
Shows Hopf fibration via projection to 3-ball.
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.
 

Teaching 2016–Present

 
College Algebra
2021–2022

Ohio State University, Newark
Calculus
2020

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

 
Corey Staten
Graduated 2018


Michael Horst
Graduated 2020

 

Service 2016–Present

 
Site Administrator, MathMeetings.net
2010 present

Vice-Chair, Faculty Assembly
2020 2021

Ohio State University, Newark Campus
Academic Affairs Committee
2017 2019

Oho State University, Newark campus
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
Presenter, Blowing Off STEAM
January 9, 2018

“Confessions of a Mathematician”
Thirty One West
Presenter, Franklinton Friday
December 8, 2017

“Snowflake Symmetry”
OSU STEAM Factory
Presenter, Ms. Cline’s 2nd grade class
December 15, 2017

“Snowflake Symmetry”
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
Organizer, Spring 2016 Midwest Topology Seminar
May 14, 2016

Ohio State University, Columbus campus
https://nilesjohnson.net/MTS
Organizer, 2016 Pi Measurement Challenge
March 13, 2016

Great Circle Earthworks, Newark, Ohio
https://u.osu.edu/piday
Presenter, Chamber of Commerce After Hours
February 18, 2016

Ohio State University, Newark campus
 

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