David Spivak

Research Scientist
Department of Mathematics

Office: Building 2, Room 180
Email: dspivak--math/mit/edu
Curriculum Vitae.

Current research projects

Technical Proposal: "Pixel matrices and other compositional analyses of interconnected systems". This is a proposal for another awarded AFOSR grant.

Technical Proposal: "Categorical approach to agent interaction". This is the proposal for the awarded AFOSR grant FA9550-19-1-0113.

Technical Proposal: Category-theoretic Approaches for the Analysis of Distributed Systems. This is the proposal for the awarded NASA grant NNH13ZEA001N-SSAT.

Other grants. These are several grant proposals, some funded, some in the pipeline, others not funded, that explain various facets of my research.

Categorical informatics. What is the underlying mathematical structure of information itself?

FQL. Functorial query language. Build your own categories, functors, and database instances, and push them around with data migration functors. (Joint with Ryan Wisnesky).

Category theory books

Category Theory for the Sciences was published by MIT Press. The book can also be purchased on Amazon. Here are reviews by the MAA, by the AMS, and by SIAM. Course materials (MIT OCW) can be found here.

Seven Sketches in Compositionality, by myself and Brendan Fong will be published by Cambridge University Press.

Past research subjects

Derived manifolds. The category of derived manifolds contains arbitrary intersections of manifolds, even if they are not transverse, while retaining enough structure so that every compact derived manifold has a fundamental class in cobordism.

Mapping spaces in quasi-categories. Joint work with Dan Dugger.

High-energy physics. A paper I coauthored with Puneet Batra and Bogdan Dobrescu.


Category theory for scientists. Taught at MIT in Spring 2013. Course materials (MIT OCW) can be found here.

Seven Sketches in Compositionality. Taught at MIT in Spring 2018, with Brendan Fong. Course materials (MIT OCW) can be found here.

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