David Spivak


Current ACT grants

Functorial Dynamics and Interaction. Using polynomial functors to model dynamical systems, decision processes, data migration, and more! (I'm completely enthralled with the category Poly.) Funded as AFOSR grant FA0995-01-20-0348. Here is an application for a potential supplement Data-driven dynamics and collective decision-making.

A book on the subject is in preparation. Idris code can be found here.

Past ACT grants

Databases and Networks. This is a 2008 proposal for the first grant I received from the ONR (N000140910466). In it, I propose to use category theory to study databases, networks, and learning. A "summary for the admiral" is here. Here is the final progress report for it.

Networking academia The above ONR grant is in some sense a more technical version of this earlier 2008 proposal, which I had earlier (unsuccessfully) submitted for a grant called "Science and the Human Condition" at the University of Oregon. The idea here is to study networks, as found in computer science, economics, linguistics, sociology, and biology, under a single mathematical framework. The document is written for a layperson. (Unfunded.)

Categorical information theory. This is a 2010 proposal for the second incarnation, N000141010841, of the above ONR grant. Here the focus has shifted to studying systems of information. A final report for this grant can be found here.

Categorical approach to agent interaction. This is a 2012 proposal to use category theory in the study of how agents communicate and interact to form higher-level agents. AFOSR grant number FA9550-14-1-0031.

Categorical informatics. This is a 2013 proposal for the third incarnation of the ONR grant, N000141310260. Here the focus has shifted to some specific problems in databases, such as updates, hierarchy, aggregation, and non-atomic fields. Here are progress reports from 2013 and 2014 and the final report.

Category-theoretic Approaches for the Analysis of Distributed Systems. This is a 2013 proposal (jointly with Honeywell) to use category theory to consider the problem of making high-assurance safety claims on systems composed of smaller systems. NASA grant number NNH13ZEA001N-SSAT. Here is the progress report for year 1. Here is NASA's final review of our work.

Categorical informatics: A functorial approach to data integration This is a proposal for an NSF III grant, submitted November 2015. (Unfunded.)

Solving Information-Integration Problems Using Category Theory. Joint with Ryan Wisnesky (co-PI). This is an NSF I-Corps grant for $50,000 to spend in Spring 2016 in order to find "product-market fit" for the new company Categorical Informatics Inc.

Pixel matrices and other compositional analyses of interconnected systems . This is a 2016 proposal for a funded AFOSR grant to study compositional analysis of systems. AFOSR grant number FA9550-17-1-0058.

Categorical approach to agent interaction: Information, Communication, Planning, and Learning. This is a 2018 proposal for a second incarnation of "Categorical approach to agent interacton". AFOSR grant number FA9550-19-1-0113.

Commons License
This work by David I. Spivak is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.