Research Scientist

Department of Mathematics

MIT

Email: dspivak--math/mit/edu

#### Pixel Array method.

Pixel Arrays **[Slides]** A talk I gave on 2016/10/26 at
MIT, in the Numerical Methods for PDE seminar, called "The Pixel
Array method for nonlinear systems, and applications to numerical
PDEs".

Pixel Arrays **[Slides]** A condensed talk I gave on 2017/07/13 at
SIAM.

#### Modular systems.

Wiring diagrams. **[Slides]** Introductory talk.

Wiring diagrams. ** [Slides]** A talk I gave on 2014/01/23 at
CMU, called "Toward a categorical foundation of functional reactive
programming".

Wiring diagrams. ** [Slides]** A similar talk I gave on 2014/02/19
at
Harvard, called "Toward a categorical foundation of functional reactive
programming".

Wiring diagrams. ** [Slides]** Adds a part about open questions;
otherwise similar talk, given at Adam Chlipala's seminar on
2014/04/15.

Materials design** [Slides]** A talk, called "A category-theoretic
approach to materials design", which I gave at the 2015 Design Theory
Workshop in Paris.

Modular systems** [Slides]** A talk I wrote, called "A mathematical
language for modular systems".

Operadic networks **[Slides]** A talk I gave in the Complex Systems Seminar
at U. Penn, called "Thinking about modularity in
networks".

Hybrid systems **[Slides]** A talk I gave at SIAM, 2017/07/12,
called "Compositional contracts for hybrid dynamical systems".

#### Database schemas are category presentations.

Databases are categories.**[Slides and Video]** A talk I gave at
Galois Inc. in
Portland on 2010/06/03. The idea is that a category is a database
schema.
Slides.

Databases are categories 2.**[Slides and
Video]** A second talk I gave at Galois Inc., on 2010/10/22. I discuss
sketches, modeling incomplete data, views and data migration via
polynomial functors, and enforcing
data types and calculated fields. I also discuss ologs.
Slides.

Categorical databases.**[Slides]** An introductory talk. I gave this talk
at an
(contractually obligatedly) undisclosed location on 2012/01/13.

Databases=Categories.**[Slides]** A talk
I gave at
MIT's CSAIL on 2010/09/16.

Databases=Categories.**[Slides]** A talk I gave at Harvard's
Programming Language
seminar on 2010/11/03.

Categorical databases. **[Slides]** This is a talk I gave on
2011/01/20 at Boston
Haskell. In it I discuss monads on database states.

Categorical databases.
**[Slides]** A talk I gave on 2012/01/18 at CMU. In it, I discuss some
relationship to lifting problems (a la Quillen model categories) and my
main open question: "how can we categorically understand the fundamental
relationship between database and algorithm?"

Category Theory as a Unifying Database Formalism **[Poster]** This
is a poster I
presented (joint with Carlo Curino)
at the New England Database Summit 2011.

Categorical
informatics. A talk I gave at NIST on 2013/06/13.

Categorical
databases. A talk I gave at Oracle on 2014/02/28.

Outlines
of similar talks. ** [Outlines]**

#### Ontologies and communication networks.

Communication networks.**[Outline]** A talk I gave in the Semantics Reading Group
(Linguistics Department) at MIT, 2010/09/15.

#### Simplicial databases.

Simplicial databases. **[Outline]**
A talk I
gave at Reed College on 2010/03/25.

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