# 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.