Research Scientist

Department of Mathematics

MIT

**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.

### Teaching

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.

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