HI THERE! I’M JOSEPH JOHNSON
I will be an Assistant Professor in the Department of Mathematics and Statistics at Carleton College. I am interested in studying nonlinear phenomena that arise in social and physical systems.
My Research
I use dynamical systems in order to model social and biological phenomena!
BIMODALITY IN ADVERTISING
In this project, we investigated competition of firms in market via advertising. We showed that under a small number of assumptions that firms will naturally split off into a name-brand group, which advertises at a high rate and generic brand group, which advertises virtually nothing.
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J.D. Johnson, A. Redlich, D.M. Abrams “A Mathematical Model for the Origin of Name Brands
and Generics.” SIAM Review 64.3 (2022): 625-639; https://doi.org/10.1137/20M1360888
EMERGENCE OF TWO SEXES
Here we developed a mathematical model to provide an argument as to how anisogamy, having sex cells of different sizes between the mating types, arose from an isogamous population, a population having the same size of sex cells.
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J.D. Johnson, N.L. White, A. Kangabire, D.M. Abrams "A Dynamical Model for the Origin of Anisogamy." Journal of Theoretical Biology 521 (2021): 110669; https://doi.org/10.1016/j.jtbi.2021.110669
MULTIMODALITY IN COUPLED OSCILLATORS
To describe synchrony of oscillators (e.g. neurons, flashing of fireflies, etc.), typically a mathematical model with attractive coupling is used. This usually leads to all the oscillators in agreement, but here we showed that we can get multiple groups of oscillators in agreement if we used repulsive coupling.
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Publications: J.D. Johnson, D.M. Abrams ``A Coupled Oscillator Model for the Origin of Bimodality and Multimodality''. Chaos 29, 073120 (2019) https://doi.org/10.1063/1.5100289
EDUCATION
APPLIED MATHEMATICS, PHD
NORTHWESTERN UNIVERSITY
Advisor: Daniel M. Abrams
Research: Multimodality in Social and Biological Systems
https://www.proquest.com/docview/2447821514?pq-origsite=gscholar&fromopenview=true
September 2015 - September 2020
APPLIED MATHEMATICS, MS
UNIVERSITY OF AKRON
Master's Thesis: Modeling Monitoring of An Industry In A Game-Theoretic Framework with Imperfect Information
August 2013 - May 2015
APPLIED MATHEMATICS, BS
UNIVERSITY OF AKRON
Double Major in Economics, Graduated Summa Cum Laude
August 2010 - May 2015
Teaching
University of Michigan
INTRODUCTION TO AGENT BASED MODELING
An introductory course to agent based modeling. I
focused on complex systems, coding in NetLogo, and modeling concepts. (2020 - 2022)
Northwestern University
MULTIVARIABLE CALCULUS
Northwestern’s EXCEL program, a 5-week summer program for
a diverse set of incoming freshmen. I developed and applied active learning techniques for this
course. (2017 - 2019)
Engineering Analysis 4 ( Head TA)
a course that covers analytical and numerical methods to solve ordinary
differential equations. This course typically has over 150 students. (2017 - 2018)
Here's a short video about understanding eigenvalues and eigenvectors geometrically!
Mulitvariable Integration and Vector Calculus (TA)
this class focuses on multiple integration in cartesian, cylindrical, and spherical coordinates, culminating with line and surface integrals.
(2016)
The University of Akron
PRECALCULUS
an introductory course to develop concepts needed for Calculus. (2014 - 2015)
INTERMEDIATE ALGEBRA
an introductory algebra course to bring students up to speed for math-
ematics at the college level. (2013 - 2014)
News
Web Articles
Student Feature - Joseph Johnson
I wrote piece about my time at Northwestern University! https://dsweb.siam.org/The-Magazine/Article/student-feature-joseph-johnson. (2017 - 2019)
Dynamics Days US 2020 Recap
I wrote a recap for Dynamics Days US 2020. It was an exciting event with many engaging talks. https://dsweb.siam.org/The-Magazine/All-Issues/dynamics-days-us-2020-recap