My primary research is in the area of
homotopy theory, specifically questions involving (monoidal)
categories, Quillen equivalences, Bousfield localization,
cellularization, algebras over (colored) operads, and coalgebras
comonads. My work has applications to (stable) homotopy theory,
category theory, equivariant homotopy theory, Goodwillie
homological algebra, motivic homotopy theory, and representation
theory. My PhD thesis was
supervised by Mark
have also done research in computer science and discrete
Under the supervision of Danny
Krizanc, my Master's thesis
settled a conjecture involving autonomous agents
moving on a graph. I have supervised undergraduate research
in computer science on the structure of
graphs, R package development, and streaming algorithms for
I have done work in statistics, with two papers so far
focusing on statistical pedagogy, and several applied
papers. I have supervised undergraduate
research projects related to spatial econometrics,
genomic modeling, data-driven journalism, and epidemiology
(specifically, the opioid epidemic in Ohio).
I have done work in economics, to create a game theoretic
the collective action problem in
revolutions, with a particular focus on the 2014 rebellion in
I have a project in progress focusing on mass shooting data
My coauthors have included Mark Hovey, Michael
Javier Gutierrez, Boris
Don Larson, Kristen Mazur, Carolyn Yarnall, Cary Malkiewich,
Merling, Luke Wolcott, Nathan Carter, Olga
Tom Bressoud, Matt Kretchmar,
Dick DeVeaux, Mahesh Agarwal, Maia Averett, Ben Baumer, Andrew
Lance Bryant, Lei Cheng, Amanda Francis, Robert Gould, Albert
Lu, Ann Moskol, Deb Nolan, Roberto Pelayo, Sean Raleigh, Ricky
Mutiara Sondjaja, Neelesh Tiruviluamala, Paul Uhlig, Talitha
Washington, Curtis Wesley, Ping Ye, Andrew Magyar, J.D.
Phillips, Kyle Prifogle, William Young, Lin Ma ('20), Lam Tran
('21), and my brother, Michael White.
I am also an active contributor to MathOverflow.
Books and Chapters
- Introduction to Data
Building from Python, with
- Statistics for Mathematicians, Chapter in Data Science for
edited by Nathan
Taylor and Francis, 2020.
- Monoidal Bousfield Localization and Algebras over Operads,
Infinite Graphs with Random Local Orientations, Wesleyan
2012. Available digitally through WesScholar,
or as arxiv
- Smith Ideals of Operadic Algebras in Monoidal Model
with Donald Yau, accepted to Algebraic and Geometric
- Homotopy theory of algebras of substitudes and their
localisation, with Michael Batanin. Transactions of the American
Mathematical Society, Volume 375, Number 5, May
2022. Available as arXiv:2001.05432.
Bousfield Localization and Algebras Over Operads. Equivariant Topology and Derived Algebra,
Cambridge University Press, pp. 179-239, 2021. Available
- VEGF-A, PDGF-BB and
engineered for promiscuous super affinity to the
improve wound healing in a model of type 1 diabetes, joint
Hubbell, Michael White, and Priscilla Briquez, Nature: Regenerative
- Substitudes, Bousfield
localization, higher braided operads, and Baez-Dolan
Forschungsinstitut Oberwolfach, Number 46, 2021:
Homotopical Algebra and Higher Structures, pp. 56-60.
- Left Bousfield Localization and Eilenberg-Moore
Michael Batanin. Homology,
Homotopy, and Applications, Volume 23, Issue 2, pp.
299-323, 2021. Available as arXiv:1606.01537.
Statistical Analysis of Drug Seizures and Opioid Overdose
Deaths in Ohio from 2014 to 2018, with Lin Ma and Lam
Tran, Journal of Student
Research, Volume 10, Issue 1 (2021).
- Right Bousfield Localization and Operadic Algebras, with
Donald Yau. Tbilisi
Mathematics Journal, Special Issue
(HomotopyTheorySpectra), pp. 71-118, 2020. Available as arXiv:1512.07570.
Alternative Approach to Equivariant Stable Homotopy Theory,
Mark Hovey. Tbilisi
Mathematics Journal, Special Issue on Homotopy Theory,
Spectra, and Structured Ring Spectra, 51-69, 2020.
Available as arXiv:1312.3846.
User's Guide Project: Looking Back and Looking Forward,
with Don Larson, Kristen Mazur, and Carolyn Yarnall. Journal of Humanistic
Mathematics, Volume 10, Issue 1, pages 411 -
- Homotopical Adjoint Lifting Theorem, with Donald Yau, Applied Categorical Structures,
Volume 27, Issue 4, 2019, pages 385-426. Available as arXiv:1606.01803.
- A Project Based Approach to Statistics and Data Science, PRIMUS, Volume 29,
Issue 9, 2019, pp. 997-1038. Available as arXiv:1802.08858.
- Arrow Categories of Monoidal Model Categories, with Donald
Yau, Math. Scandinavica,
125(2), pp. 185-198, 2019, available as arXiv:1703.05359.
- An Overview of Schema
Theory, The Graduate Journal of
Mathematics, Volume 3, Issue 2, 2018, 37-59. Available
- Encoding Equivariant
Commutativity via Operads, with Javier Gutierrez, Algebraic and Geometric
Topology, Volume 18, Number 5, 2018, 2919-2962.
Available as arXiv:1707.02130.
- Bousfield Localization
and Algebras over Colored Operads, with Donald Yau. Applied Categorical
Structures, Volume 26, Issue 1, 2018, pages 153-203. Available as arXiv:1503.06720.
Structures on Commutative Monoids in General Model
Categories. Journal of Pure and Applied Algebra,
Volume 221, Issue 12, 2017, pages 3124-3168. Available as
- Curriculum Guidelines
Undergraduate Programs in Data Science, with Richard De
Veaux, et al.
Report from Undergraduate Faculty Group at Park City
Review of Statistics, Vol. 4, 2017, pages 15-30. Available as arXiv:1801.06814.
Stabilization via (Semi-)Model Categories of Operads,
with Michael Batanin. In Interactions between Representation Theory,
Algebraic Topology, and Commutative Algebra, ed.
Dolors Herbera, Wolfgang Pitsch, and Santiago Zarzuela, Research
Perspectives CRM Barcelona, Volume 5, 2015, pages 175-179.
Birkhauser, DOI 10.1007/978-3-319-45441-2.
User's Guide Project:
Giving Experiential Context to Research Papers, with
Mona Merling, Frank Lucas Wolcott, and Carolyn Yarnall. Journal of Humanistic
Mathematics, volume 5, number 2, 2015.
- A Rational Choice Model of the Rise of Self-Proclaimed
States Encompassed in Weak Post-Soviet Economies, with Olga Nicoara. 2015 Annual Meetings of the Public
- A user's guide:
Monoidal Bousfield localizations and algebras over
Mathematical Users Guides, Vol. 1, 2015.
Available as arXiv:1801.03191.
- White Paper Research
(title is classified), Internal
NSA Journal, Division R6,
Investigation into the
Structure of Digroups (with
A. Magyar, J.D. Phillips, K. Prifogle, and W. Young), Proceedings
of the Wabash Summer
Institute in Algebra,
- Left Bousfield Localization without Left Properness, with
- Comonadic Coalgebras and left Bousfield Localization, with
Yau, available as arXiv:1805.11536.
- A variant of a Dwyer-Kan theorem for model categories,
with Boris Chorny,
submitted, submitted, available as arXiv:1805.05378.
- Right Bousfield Localization and Eilenberg-Moore
Categories, with Donald
Yau. Submitted. Available as arXiv:1609.03635.
in Various Categories of Manifolds, December 2012.
- Model Structures on
non-Reduced Operads and the Commutative Monoid Axiom, with
- Model structures on
and algebras from a global perspective, with Michael
- Derived localisation
Grothendieck construction, with Michael Batanin.
- Localization and Cellularization for Motivic Symmetric Spectra, with Carles Casacuberta.
- A short note on
- The Random
Basic Walk on Infinite Graphs.
- Parallel Search on
Intersection Graphs, with Jessica Tang.
- Model structures for
relative stable module category, with Daniel Bravo and
- Abelian Left Bousfield
localization, with Daniel Bravo.
- On multiplicative
Research I have
- An Overview of Spatial
Econometrics, Alex Tybl, arxiv
1605.03486 and Social
Research Network (SSRN) number 2778679.
- Using Genomics to
Disabilities, Trevor Masters.
- Parallel Search on
Intersection Graphs, with Jessica Tang.
- Data Driven Journalism
Opioid Epidemic (2019), with Lin Ma and Lam Tran.
- Streaming Statistical
(2019) with Colin Smith.
Ideas for Undergraduate Research
- RC Good Fellowship, Convenient
Combinatorial Categories of Topological Spaces,
Principal Investigator, spring 2022. Funding for a
one-semester research leave.
- COVID Re-engagement Grant, The McClure-Smith Conjecture, Principal
Investigator, fall 2021. Funding for a summer visit to
Michael Batanin in Prague, Czech Republic.
- Pedagogical Practice Projects Grant, Inviting Data Analytics Majors
Introductory Computer Science, Denison University,
- Center for Teaching and Learning, funding for Pedagogy and Resilience
group, Denison University, 2019-2020.
- Pedagogical Practice Projects Grant, SAGE Labs in Calculus,
University, spring 2017.
- Center for Teaching and Learning, funding for Teaching Statistical Concepts
reading group, Denison University, 2016-2017.
- Pedagogical Practice Projects Grant, Statistical Modeling,
University, spring 2016.
- Center for Mathematics and Scientific Computation, Equivariant cellularization
nullification, co-Principal Investigator with Boris
funding for research visit in July 2015.
- Denison University Research Table Grant, Ethics in Cyber Space,
co-Principal Investigator with Joan Krone and John McHugh.
interdisciplinary research, undergraduate research,
pedagogy, and to bring several external speakers to campus
- Project NExT Fellow, 2015-2016.
- National Science Foundation, East Asia and Pacific Summer
Institutes for U.S. Graduate Students (EAPSI): "Studying the
between Localization and Categorical Algebra via Algebraic
award number IIA-1414942.
Funded to be a visiting scholar at Macquarie University
Michael Batanin. Additional funding provided by Australian
Student Travel Grant for travel to Joint Mathematics
Meetings, January 2014.
Foundation Travel Grant for Type Theory, Homotopy
and Univalent Foundations conference held in Barcelona,
- AMS Funding to start Graduate
Chapter at Wesleyan, 2013.
an undergraduate I was lucky to be part of two REUs, so
in the value of research for undergraduates. I maintain
of projects on which I would be happy to collaborate
undergraduates and early graduate students in
mathematics or computer
science. If you're interested in seeing this list please
To Denison students: I will happily take on research
applied statistics at any time, ideally during the
semester. For pure
mathematics or computer science, my research interests
tend towards the
abstract. Thus, research with me will likely best serve
interested in graduate school. For such students, the
best time to do
research with me is during the summer after your
sophomore year, or as
an independent study in your junior or senior year. The
your junior year would be best spent at an REU, to best
yourself for applying to graduate school.
A nice collection of open problems about popular games
can be gleaned