I’m a fifth year graduate student at Johns Hopkins University. My advisor is Emily Riehl. It's me!

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)!

I teach and TA. Follow this link for more info.

Preprints

___, 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

___, Good Fibrations through the Modal Prism, arXiv:1908.08034, 2019

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

Publications

Math

___, 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