Broadly, I am interested in applications of category theory, especially higher category theory, to different areas of mathematics and particularly physics. Category theory is a branch of mathematics that not only abstracts mathematical structures common to several different fields but is also a general theory of processes. It also serves as a language that connects different fields.
So far I have done work in the following areas. If you would like to know more information, click on the corresponding category, where I describe more about the subject and my specific interests in the area. Below each category are publications or preprints for those categories. The subjects are listed in most recent order of activity.
- “Discrete probabilistic and algebraic dynamics: a stochastic Gelfand-Naimark Theorem,” Submitted
Algebraic quantum theory
- “Stinespring’s construction as an adjunction,” Submitted (2018)
- “From observables and states to Hilbert space and back: a 2-categorical adjunction,” Applied Categorical Structures, Vol. 26, Issue 6, pp 1123-1157 (2018). Available as https://link.springer.com/article/10.1007/s10485-018-9522-6 and
Higher gauge theory
- “Two-dimensional algebra in lattice gauge theory,” Accepted in Journal of Mathematical Physics
- “Gauge invariant surface holonomy and monopoles,” Theory and Applications of Categories, Vol. 30, No. 42, pp 1319-1428 (2015)
- “Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps” with Karen K. Y. Lee, Yehuda Avniel, and Steven G. Johnson, Phys. Rev. B 81, 155324 (2010)