Michael Stone's Research Activities

Updated October 26, 2006.

Site under construction. If you'd like to see the poster, read the notebook, or generally find out what happened, please contact me at mstone [AT] sccs.swarthmore.edu. The bibliography is available at Michael Stone's CiteULike Bibliography.

Research Summary

The goal of this research project was to make sense of an alternative diagram language for representing 2-categorical constructs. The project consisted of several phases including a systematic exploration of the diagram language by means of category-theoretic and combinatorial exercises, a literature search for related work in neuroscience, physics, and computer science, and careful study of the diagram's explanatory value in the domains of linear algebra and the denotational semantics of programming languages. The project culminated in the creation of a diagram-heavy poster on programming language semantics, an electronic notebook of the researcher's observations, and an extensive electronic bibliography for jumpstarting future researchers. The research was significant because it demonstrated the power of the diagrams to illustrate important mathematical abstractions like monads in material intended for a non-specialist audience. For example, a professor of mathematics might use this research to help produce new and better pedagogical resources for explaining the 2-categorical basis of many common abstractions. Since the diagrams are useful for performing and checking categorical computations, a student of mathematics may find the work helpful in approaching their own categorical exercises. Finally, the work demonstrates that researchers in fields that use category theory (such as physics, computer science, and biology) might find the diagrams helpful in explaining their research to a broader audience.

Bibliography: Michael Stone's CiteULike Bibliography
Poster (letter-size): Sigma Xi Poster
Poster (full-size): Sigma Xi Poster
More information: see above
Contact: see above
Thesis Plans: I am an Honors student but I do not intend to write a thesis.