# 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, E

_{n}-Monoidal Categories, and Algebraic K-Theory Joint with Donald Yau. Accepted to Mathematical Surveys and Monographs, American
Mathematical Society.

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

Joint with Nick Gurski and Angélica Osorno. To appear in Higher Structures.

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

^{−1}S 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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