Department of Mathematics

MIT

Email: dspivak--math/mit/edu

Databases and Networks. This is a 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 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 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 informatics. This is the 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.

Categorical approach to agent interaction. This is a 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.

Category-theoretic Approaches for the Analysis of Distributed Systems. This is a 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.

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 proposal for a funded AFOSR grant to study compositional analysis of systems.

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