David Spivak

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.






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