David Spivak

Research Scientist
Department of Mathematics
MIT

Office: E17-417
Email: dspivak--math/mit/edu
Curriculum Vitae.

Purpose: I study information and communication, working towards a mathematical foundation for interoperability.

Current research projects


Technical Proposal: "Categorical informatics". This is the proposal for the awarded ONR grant N000141310260.

Technical Proposal: "Categorical approach to agent interaction". This is the proposal for the awarded AFOSR grant FA9550-14-1-0031.

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 book


MIT Press has published "Category theory for the sciences". The book can also be purchased on Amazon. Here are reviews by the MAA, by the AMS, and by SIAM.

Free HTML version: not as nice to read, but free to the world, on the MIT Press website. An older version, entitled "Category theory for the scientists", can be found here.

Course (Spring 2013). Course webpage.

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.

Other stuff


Miscellaneous files Includes some papers of mine and others (some brief or unfit for publication, but possibly of interest), a program for doing calculations in a group-ring, some LaTeX guides I use, and other random stuff.

Links


MathSciNet.
arXiv.
Category theory reprints.
Dan Dugger's page.
Jacob Lurie's page .
John Baez's blog .
MIT Math department.
MIT Library.
MIT.




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