I’m a post-doc working at the Center for Topological and Quantum Systems at NYU Abu Dhabi. I did my PhD with Emily Riehl at Johns Hopkins.

I’m generally interested in what it means to be a *thing*, but particularly interested in (higher) category theory, homotopy type theory, and cohesion. I have been writing a book on categorical systems theory which is currently in its 0th draft — use at your peril (but enjoy)!

## Preprints

___, *Orbifolds as Microlinear Types in Synthetic Differential Cohesive HoTT*, arXiv:2205.15887, 2022

___, *Modal Fracture of Higher Groups*, arXiv:2106.15390, 2021

___, D. Spivak, *Dirichlet Functors are Contravariant Polynomial Functors*, arXiv:2004.04183, 2020

___, *A Yoneda-Style Embedding for Virtual Equipments*, arXiv:2003.02124, 2020

___ , *String Diagrams for Double Categories and Proarrow Equipments*, arXiv:1612.02762, 2016

## Publications

### Math

___, *Good Fibrations through the Modal Prism*, in Higher Structures (2022), arXiv:1908.08034, 2019

___, *Double Categories of Open Dynamical Systems (Extended Abstract)*, arXiv:2005.05956, 2020

D. Spivak, ___, B. Fong, *Behavioral Mereology*, arXiv:1811.00420, 2018

E. Hanna, C. Lynch, ___, C. Richardson, *Finding Intruder Knowledge with Cap Matching*, in Guttman J., Landwehr C., Meseguer J., Pavlovic D. (eds) Foundations of Security, Protocols, and Equational Reasoning. Lecture Notes in Computer Science, vol 11565. Springer, Cham.

### Other

P. Thibodeau, ___ , S. Flusberg, *Similarity-Based Reasoning is Shaped by Recent Learning Experience*, in *Proceedings of the 38th Annual Conference of the Cognitive Science Society*. Austin, TX: Cognitive Science Society. 2016

## Notes

___, *Cartesian Factorization Systems and Grothendieck Fibrations*, arXiv:2006:14022, 2020

D. Spivak, ___, *Dirichlet Polynomials Form a Topos*, arXiv:2003.04827, 2020

*Notes on Homology in Characteristic One*, from a course given by Katia Consani (and with material from Emily Riehl) in 2017.

## Talks and Slides

*Modal Fracture of Higher Groups*, at HoTT/UF 2021, [slides]

*Modal Fibrations in Homotopy Type Theory*, at University of Augsburg, 2021, [slides]

*Modal Fibrations in Homotopy Type Theory*, at the EPFL Topology Seminar, 2021, [slides]

*Modal Fracture of Higher Groups*, at the CMU-HoTT Seminar, 2021, [slides]

*Paradigms of Composition*, at the MIT Category Seminar, 2020, [slides]

*Paradigms of Composition*, at the Calgary Peripatetic Seminar, 2020, [slides]

*Getting equipped for formal category theory*, at the Johns Hopkins Category Seminar, 2020

*Double categories of Open Dynamical Systems*, at ACT 2020, 2020, [video] [slides]

*Behavioral Merelogy: a modal logic for passing constraints*, at ACT 2020, 2020, [video] [slides]

*Higher Schreier Theory*, at HoTTEST 2020, 2020, [video] [slides]

*Double Categories of Open Dynamical Systems*, at the Coimbra Algebra, Logic, and Topology seminar, 2020, [slides]

*Homotopy Type Theory for doing Category Theory*, at the MIT Category Seminar, 2020, [slides] [video]

*Open Dynamical Systems, Trajectories, and Hierarchical Planning*, at the MIT Category Seminar, 2020, [video]

*A General Definition of Open Dynamical System*, at the MIT Category Seminar, 2020, [video]

*At a stalk, in general, and other ways of being true*, at the Johns Hopkins Category Seminar, 2019, [notes]

*A sheaf of rings is a ring of sheaves, and other tales from algebra on the inside*, at the Johns Hopkins Category Seminar, 2019, [notes]

*Higher Groups in Homotopy Type Theory*, for my Oral Exam at JHU, 2019, [slides]

*Good Fibrations through the Modal Prism* at HoTT 2019, 2019, [slides]

*How do you identify one thing with another* at Cornell Topology Fesitval, 2019, [slides]

*generatingfunctorology*, at the Johns Hopkins Category Seminar, 2019

*Degrees, Dimensions, and Crispness*, at Geometry in Modal HoTT, 2019 [slides] [video]

*Logical Topology and Axiomatic Cohesion*, at Geometry in Modal HoTT, 2019 [slides] [video]

*The logic is coming from inside the category*, at the Johns Hopkins Category Seminar, 2018

*Towards A¹ Homotopy Type Theory*, at the CMU HoTT Seminar, 2018

*What is a Thing?*, at MIT Categories Seminar, 2018
[slides]

*The Yoga of Four Operations*, at the Johns Hopkins Category Seminar, 2018

*String Diagrams for (Virtual) Proarrow Equipments*, at CT 2017, 2017 [slides] [abstract]

*Weighted (Co)Limits*, at CT 2017 with the Kan Extension Seminar, 2017 [slides]

*String Diagrams, Categories, and Enrichment*, for Honors thesis requirement at Oberlin, 2016 [slides]

*Thinking Recursively, Rethinking Corecursively*, for Oberlin Philosophy department, 2015 [slides] [abstract]

## Blog Posts

*Graphical Regular Logic*, with Sophie Libkind, on the *n*-category Café

*A Graphical Calculus for Proarrow Equipments*, on the *n*-Category Café

*Gluing Together Finite Shapes with Kelly*, on the *n*-Category Café, written for the Kan Extension Seminar

*Enrichment and its Limits*, on the *n*-Category Café, written for the Kan Extension Seminar

## History

2017 - *now*: Johns Hopkins University

Spring 2015: Central European University

Fall 2015: Budapest Semesters in Mathematics

2012 - 2017: Oberlin College