David Spivak

Senior Research Scientist and Institute Fellow at Topos Institute

Curriculum Vitae

Email: dspivak@gmail.com

Current research projects

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

Structure and dynamics of working language Using polynomial functors to account for how language works, in the sense of physics. This grant has been recommended for funding, but has not yet started.

Introductory books on Applied Category theory

Category Theory for the Sciences was published by MIT Press, also available 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. This material has been published by Cambridge University Press as An Invitation to Applied Category Theory by Brendan Fong and David I. Spivak. This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Brendan Fong and David Spivak 2019. Also available on Amazon.
Here is a review by the MAA and a review by Acta Crystallographica.
Course materials (MIT OCW) can be found here.

Past research subjects

Applied Category Theory. Various ACT grants, some funded and others not.

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.

Values Statement

Values Statement. This is a first attempt to convey the values that seem to motivate me.

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