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People / David Spivak

Senior Scientist and Institute Fellow & Treasurer (US)

About

David Spivak leads the Collective Intelligence research group at Topos, after a decade as a researcher at MIT. Since his PhD from UC Berkeley in 2007, he has worked to bring category-theoretic ideas into science, technology, and society, through novel mathematical research, through collaboration with scientists and engineers from disciplines including Materials Science, Chemistry, Robotics, Aeronautics, and Computer Science. His mission at Topos is to help develop the ability for people, organizations, and societies to make sense of—and hence to serve—the systems which sustain them.

Personal website
http://dspivak.net/

Grants

  • Current: Structure and dynamics of working language and Accountable Metaphysics.

Talks

Here are slides and recordings from talks given since starting at Topos.

  • “Poly: A category of remarkable abundance”, from 2021 Topos Colloquium. [Slides] [Video]
  • “Polynomials and the dynamics of data”, from 2021 Seminario de Categorias at UNAM. [Slides] [Video]
  • “The polynomial abacus”, from 2021 Workshop on Polynomial Functors. [Slides] [Video 1] [Video 2]
  • “Learners’ Languages”, from 2021 Topos Internal Seminar. [Slides] (Video not available)
  • “Functorial aggregation”, from 2022 Workshop on Polynomial Functors. [Slides] [Video]
  • “Some applications of polynomial functors”, from 2022 Pisa meeting on applications of category theory. [Slides]
  • “Polynomial Functors and Shannon Entropy”, from a 2022 talk at the Symposium on Categorical Semantics of Entropy. [Slides] [Video]
  • “Sense-making: Accounting for intelligibility”, from 2022 IPAM Workshop on Mathematics of Collective Intelligence. [Slides] [Video]
  • “Dynamic interfaces and arrangements: An algebraic framework for interacting systems”, from a 2022 talk in Mike Levin’s seminar. [Slides] [Video]
  • “Is Poly the true language of computation?”, my 2022 AFOSR Review talk. [Slides]
  • “Dynamic Interfaces and Arrangements”, from a 2022 talk at the Active Inference Instute. [Slides] [Video]
  • “Dynamic organizational structures”, from a 2022 talk at the NASA “Prebiotic Chemistry and Evolution of the Early Earth” PCE3 workshop. [Slides]
  • “What are we tracking? How category theory puts thinking on rails”, from a 2022 tutorial at the NIST Compositional Structures in Systems Engineering and Design Workshop. [Slides]
  • “Poly is an unreasonably effective abstraction; Might it relate to healthy systems?”, from the 2023 Finding the Right Abstractions for Healthy Systems (FRA2) workshop. [Slides]
  • “Dynamic organizational systems: From deep learning to prediction markets”, from a 2023 talk in Categories for AI. [Slides]
  • “Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems”, from a 2023 talk in Category Theory for Consciousness Science. [Slides] [Video]
  • “Applied Category Theory: Towards a hard science of interdisciplinarity”, from a 2023 talk in the Society for Multidisiciplinary and Fundamental Research summer school. [Slides] [Video]
  • “All Concepts are Cat^#”, a talk at ACT 2023 on a paper joint with Brandon Shapiro and Owen Lynch. [Slides]
  • “All my relations: Contributing to a fabric of belonging”, a talk at AGI2024. [Slides] [Video]
  • “Structure and Dynamics of Working Language”, my 2024 AFOSR Review talk. [Slides]
  • “Plausible Fiction: Accounting for Actualizing Potential”, a 2024/11/05 talk at IPAM’s Naturalistic Approaches to Artificial Intelligence. [Slides] [Video]
  • “Plausible Fiction: Tending Actualizes Potential”, a 2024/12/02 talk for the MIT CEE course ACT4ED. [Slides] [Video]

Blog posts

Title Date
Discrete vs. filtered accessibility and presentability 2026-09-24
Who cares about a computation? 2026-09-22
Neural wiring diagrams for message passing in multiscale organizations 2024-11-08
Plausible fiction 2024-08-27
A polynomial account of Bayesian update 2024-08-12
Poly @ Work 2024 2024-03-27
Poly-morphic effect handlers 2024-01-03
Solving problem-solving 2023-11-13
Lie groups induce Hopf monoids in Poly 2023-10-26
Powers of polynomial monads 2023-09-21
A nuclear adjunction between Poly and Dir 2023-07-21
Dialogue on a mathematical approach to the good 2023-07-11
Natural transformations between cofunctors 2023-05-26
Spooling out syntax from behavior 2023-04-24
Lotteries: a constructive version of the distributions monad 2023-03-23
Category theorists welcome self-learners in a new outreach panel 2023-03-09
Promonoidal categories and wiring diagrams 2023-01-31
Lenses are semi-monads, maybe lenses are monads 2022-12-20
Where matter and pattern meet 2022-11-07
When you light up, I light up 2022-10-28
Nate & Jesse’s adjoint 5-tuple 2022-09-29
It’s Proly like Poly but better 2022-08-04
A 15-year history of my research program, in 10 minutes 2022-07-07
Graphs in Poly 2022-06-16
An account of sense-making 2022-06-03
The “artificial” distinction 2022-05-18
Co-design of dynamical systems 2022-04-06
2022 Workshop on Polynomial Functors 2022-03-29
Creating mathematics 2022-03-25
Poly makes me happy and smart 2022-01-19
Creating new categories from old: Selection categories 2021-12-30
Deep neural networks as nested dynamical systems 2021-11-05
Poly inside Poly 2021-09-22
Dirichlet polynomials and entropy 2021-07-25
Jump monads: from conjugation to dependent types 2021-07-01
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