Accounting for our inventiveness
NITMB Colloquium, 2026-03-17
Slides (PDF)
Keywords: Remembering how and why are we here, High-precision energy routing, Lightning, hurricanes, and life, Bacterial machinery, Mate selection: using more intelligence, Accounting, Wiring diagrams, The category of polynomial functors
Achieving answerability
NITMB: Expanding the Palette of Mathematics in Biology, 2026-01-23
Slides (PDF)
An attempt to explain category theory to biologists in 15 minutes
NITMB: Expanding the Palette of Mathematics in Biology, 2026-01-21
Slides (PDF) | Video (YouTube)
Keywords: Why are we here?, Category theory is the math of math, Operations and relations, Popper's objection, CT is the gateway to pure mathematics, Operads, Operad 2: hierarchical protein materials, Operad 3: wiring diagrams
The double category Int(Poly_+) models control flow and data flow
Topos Berkeley Seminar, 2025-07-15
Outline (PDF)
Plausible Fiction: Tending Actualizes Potential
MIT CEE: ACT4ED, 2024-12-02
Slides (PDF) | Video (YouTube)
Keywords: Plausible Fiction, What can we count on?, Contextualizing care, Persistence, dissolution, and recombination, Accounting systems, Petri nets, Operad algebras, Karmic loops
Plausible Fiction: Accounting for Actualizing Potential
IPAM Naturalistic Approaches to AI, 2024-11-05
Slides (PDF) | Video (YouTube)
Keywords: Plausible Fiction, What can we count on?, Contextualizing care, Persistence, dissolution, and recombination, Accounting systems, Petri nets, Operad algebras, Karmic loops
How should one govern a plausible fiction platform?
MathGov, 2024-10-09
Outline (PDF)
``All my relations'' Contributing to a fabric of belonging
AGI 2024, 2024-08-15
Slides (PDF) | Video (YouTube)
Keywords: How this talk will go, Collective sensemaking, The computer, Abstraction: extraction and application, Interfaces for tasks and outcomes, The algebra of interfaces, Application, What are we driving at?
The Polynomial Abacus
FMCS 2024, 2024-07-09
Slides (PDF)
Keywords: My personal history with math, Poly for experts, Pleasing aspects of Poly, Making sense of the results, Bicomodules are parametric right adjoints, Gambino-Kock's framed bicategory Poly, Moore machines as maps in Poly, Cellular automata as algebras in
Pattern runs on matter: The free monad monad as a module over the cofree comonad comonad
ACT 2024, 2024-06-17
Slides (PDF)
Keywords: What's going on here?, Polynomial functors, Polynomial functors and trees, Monads and comonads, The cofree comonad \cofree_p, Tree representation of \free_p and \cofree_p, Interactions between \free_- and \cofree_-, How it works
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Princeton Neuroscience of Cognitive Control and Astera, 2024-04-17
Slides (PDF)
Keywords: Mathematical fields as accounting systems, This is the subject of the talk, Our interfaces, Recalling all the keywords we'll use, Semantics of polynomial operations, Dynamics, Deep learning, Active inference as dynamic organizational structure
Applied Category Theory: Towards a hard science of interdisciplinarity
Princeton Neuroscience of Cognitive Control and Astera, 2024-04-10
Slides (PDF)
Keywords: A road to true interdisciplinarity, Mathematical fields as accounting systems, Popper's objection, What are compositional operations?, Formal definition of operad, Operad 3: probabilities, The operad of sets, Deep learning, prediction markets, organizations
How can math promote life?
Annual Mathematics and Philosophy Lecture, University of Calgary, 2024-03-07
Slides (PDF)
Keywords: Bridging ancient conceptions of the good, Dynamic arrangements, Mathematical fields as well-ruled accounting systems, Perspectives on category theory (I), Why are we here?, An accounting system for interfaces, Existing mathematics for interfaces, Nesting arrangements
Category Theory in Science and Engineering
Caltech, Special Seminar in Mechanical and Civil Engineering, 2023-12-14
Slides (PDF)
Keywords: Mathematical fields as accounting systems, Category theory as conceptual stem-cell, What are compositional operations?, Formal definition of operad, Operad 3: probabilities, Andrea Censi's Co-design, Lenses and open dynamical systems, Dynamic operads (Joint with Brandon Shapiro)
Applied Category Theory: Towards a hard science of interdisciplinarity
Chevron Systems Engineering Community of Practice, 2023-10-11
Slides (PDF)
Keywords: A road to true interdisciplinarity, Mathematical fields as accounting systems, Popper's objection, What are compositional operations?, Formal definition of operad, Operad 3: probabilities, The operad of sets, Deep learning, prediction markets, organizations
All concepts are Cat^#
Applied Category Theory 2023, 2023-08-04
Slides (PDF)
Keywords: All concepts?, What is Poly?, What is Cat^#?, Three homes for categories, The most familiar: -algebras, Common complaints about Poly, Dynamic functions, Dynamic arrangements
Applied Category Theory: Towards a hard science of interdisciplinarity
Society for Multidisciplinary and Fundamental Research, Interdisciplinary School, 2023-07-25
Slides (PDF) | Video (YouTube)
Keywords: A road to true interdisciplinarity, Mathematical fields as accounting systems, Popper's objection, What are compositional operations?, Formal definition of operad, Operad 3: probabilities, The operad of sets, Deep learning, prediction markets, organizations
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Category Theory for Consciousness Science, 2023-04-16
Slides (PDF) | Video (YouTube)
Keywords: Accounting, The morphology of collective sense-making, Settling accounts, How the math fits in, Combinatorics of polynomial morphisms, Wiring diagrams, Moore machines, Mealy machines, and coalgebras, ANNs in terms of
Dynamic organizational systems: From deep learning to prediction markets
Categories for AI, 2023-03-23
Slides (PDF) | Video (YouTube)
Keywords: Unreasonable effectiveness, Combinatorics of polynomial morphisms, Lenses, Moore machines, and Mealy machines, Moore machines and wiring diagrams as lenses, Databases and data migration, Recalling the internal hom for Poly, Definition of, Prediction markets in terms of
The Microservices Operad –OR– the free monad monad is a module over the cofree comonad comonad
Topos Berkeley Seminar, 2023-02-21
Outline (PDF)
Poly is an unreasonably effective abstraction; Might it relate to healthy systems?
Finding the Right Abstractions for Healthy Systems, 2023-01-09
Slides (PDF)
Keywords: Sense-making, Interfaces and interaction, Operations: +,x,x,,[-,-],--, Depicting Moore machine interfaces, Category theory in Computer Science, Dependent type theory, The ``scientist category'', Meeting the moment
Category theory is living language
Joint Mathematics Meetings, Special Session on Applied Category Theory, 2023-01-05
Slides (PDF)
Keywords: Sense-making, Accounting systems, The structure and dynamics of working language, Matter and pattern, ACT as living language, Spencer's graph, Using ACT to make sense, What's coming and who benefits?
Effects Handlers and Bicomodules
Topos Berkeley Seminar, 2022-12-12
Outline (PDF)
What are we tracking? How category theory puts thinking on rails
NIST, Compositional Structures in Systems Engineering and Design Workshop, 2022-11-03
Slides (PDF)
Keywords: Tracking values, Mathematical fields as accounting systems, Finding the right abstractions, Summarizing and concluding this example, Joey Hirsch's Shakshuka recipe, Another ACT-SME dialogue, Best practices for the interaction, Best practices for the SME
Dynamic organizational structures
NASA Prebiotic Chemistry and Evolution on the Early Earth (PCE3), 2022-10-20
Slides (PDF)
Keywords: Mathematical fields as accounting systems, My understanding of PCE3, Dynamic organizational structures, Open dynamical systems, Wiring diagrams and interaction patterns, Mode dependent interaction, More detail on dynamic organizational structures, Applications to PCE3
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Active Inference Institute, 2022-09-13
Slides (PDF) | Video (YouTube)
Keywords: Mathematical fields as accounting systems, This is the subject of the talk, Our interfaces, Recalling all the keywords we'll use, Semantics of polynomial operations, Dynamics, Deep learning, Active inference as dynamic organizational structure
Polynomial Functors and Shannon Entropy
ACT 2022, 2022-07-19
Slides (PDF)
Keywords: The overwhelming abundance of Poly, Entropy in terms of Poly, What is a morphism of polynomials?, Fundamental invariants, Derivatives and the bifibration, ppis distributive, Taking stock, The categorical partition function and entropy
The free monad, cofree comonad, and topological space associated to a polynomial
Topos Institute, Berkeley Seminar, 2022-06-14
Outline (PDF)
Dynamic Interfaces and Arrangements: An algebraic framework for interacting systems
Allen Discovery Center, 2022-06-07
Slides (PDF) | Video (YouTube)
Keywords: Mathematical fields as accounting systems, This is the subject of the talk, Our interfaces, Recalling all the keywords we'll use, Semantics of polynomial operations, Dynamics, Deep learning, Anatomical compilers
Polynomial Functors and Shannon Entropy
Symposium on Categorical Semantics of Entropy, 2022-05-13
Slides (PDF) | Video (YouTube)
Keywords: The overwhelming abundance of Poly, Poly for experts, What is a morphism of polynomials?, Fundamental invariants, Derivatives and the total space, Total space as distributive, The categorical partition function and entropy, A geometric viewpoint on Shannon entropy
Some applications of polynomial functors
University of Pisa, Computer Science Department, 2022-04-06
Slides (PDF)
Keywords: All roads lead to Rome; what did Rome have??, Getting to know Poly: the lens pattern, Today: introduce Poly in terms of its applications, Deeper look at objects and morphisms in Poly, Various notions of dynamical system, Monoidal closure of Poly, More general interfaces, Comonoids and bicomodules in Poly
Functorial Aggregation
Workshop on Polynomial Functors, 2022-03-18
Slides (PDF) | Video (YouTube)
Keywords: Why think about databases?, Querying and aggregating, Aggregation poses a ``purity of methods'' problem, Dirichlet product x and its closure, and Span as subequipments of, Adjoint prafunctors, Transposing a span, ``oppositing'' a category, Minor difficulty during talk
Sense-making: accounting for intelligibility
Mathematics of Collective Intelligence, 2022-02-19
Slides (PDF)
Keywords: Mathematical fields as accounting systems, The morphology of collective intelligence, Sense-making: the pun that wasn't, Settling accounts, The operad idea, Interaction patterns, What algorithm works?, Governance, accountability, and sense-making
Categorical Interaction in the Polynomial Ecosystem
Seminar on Categorical Interaction, 2022-01-25
Slides (PDF)
Keywords: An emerging subfield of ACT, The lens pattern, Polynomial functors are amazing, Unpacking in the Haskell case, Dynamical systems in terms of Poly, Wiring diagrams, Adaptive interaction patterns, Categorical databases
Learners' languages
Topos Internal Seminar, 2021-09-21
Slides (PDF)
Keywords: Definition and terminology of Poly, Properties of internal hom, Interaction pattern example: wiring diagrams, Characters, Learners are coalgebras, The -algebra of 0-ary morphisms, Gambling games in, Rayleigh-B\'enard convection
The Polynomial Abacus
Workshop on Polynomial Functors, 2021-03-15
Slides (PDF) | Video Part 1 | Video Part 2
Keywords: My personal history with math, Poly for experts, Pleasing aspects of Poly, Making sense of the results, Bicomodules are parametric right adjoints, Gambino-Kock's framed bicategory Poly, Moore machines as maps in Poly, Cellular automata as algebras in
Polynomials and the dynamics of data
Seminario de categorias UNAM, 2021-02-17
Slides (PDF) | Video (YouTube)
Keywords: My personal history with math, Poly for experts, Notation, Comonoid maps are ``cofunctors'', Moore machines, Other sorts of dynamical systems, A Poly-oriented view on metaphysics, The lessons of history?
Poly: a category of remarkable abundance
Topos Colloquium, 2021-02-04
Slides (PDF) | Video (YouTube)
Keywords: My personal history with math, Toward metaphysics, The category of polynomials, Comonoids in (Poly,,), The framed bicategory, Moore machines as maps in Poly, Categorical databases, Future work
Applied Category Theory: Mathematics for Interdisciplinary systems modeling
PNNL, 2021-02-02
Slides (PDF)
Keywords: A road to true interdisciplinarity, Our historical moment, Operad 1: wiring diagrams, Operad 3: probabilities, Wiring diagram operads, similar to \#1, Multiple algebras for wiring diagrams operad, Equations and wiring diagrams, Application: smart grid
A Tutorial on Category theory: Part 1: pure and classical
Finding the Right Abstractions, Topos Institute, 2021
Slides (PDF)
Keywords: A bit of history, Orders, Rules of matrices, Example: vertices and paths in a graph, Example: dimensions and matrices, Make your own, Coproducts and products, Traced monoidal categories
Cultivating Strategies
Finding the Right Abstractions, Topos Institute, 2021
Slides (PDF)
Keywords: We are gathered here today..., Cultivating strategies, Instincts, Schmidhuber's notion of beauty, The AI transition, A useful abstraction: dynamical systems, Recruitment and vibing?, Philosophy with a lifeline
Poly: an abundant categorical setting for mode-dependent dynamics
ACT 2020, 2020-07-07
Slides (PDF)
Keywords: A little personal history, What is a polynomial?, Notation, Four interacting monoidal structures, Moore machines, Depicting Moore machine interfaces, Poly and mode-dependent dynamics, Comonoids in (Poly,o,)
Polynomials: from dynamics to databases
Tallinn CS Theory Seminar, 2020-06-25
Slides (PDF)
Keywords: Names for Poly, The category of polynomials, Four interacting monoidal structures, Moore machines as lenses, Moore machines and wiring diagrams as lenses, Example, Comonoids in Poly are categories (Ahman-Uustalu), Data migration
``All my relations'' Contributing to a fabric of belonging
AGI 2020, 2020-06-12
Slides (PDF)
Keywords: How this talk will go, Collective sensemaking, The computer, Abstraction: extraction and application, Interfaces for tasks and outcomes, The algebra of interfaces, Application, What are we driving at?
Internal probability valuations
Categorical Probability and Statistics, 2020-06-07
Slides (PDF)
Keywords: What is the mathematical structure of story?, Evaluation is local in Go, Running example 1: space of Go rectangles, Logic in a topos, An internal space for Go, Semantics of lower reals, Valuations on behavior types, Families of valuations
Polynomial functors II: Seven wonders of the composition product
MIT Categories Seminar, 2020-05-28
Slides (PDF)
Keywords: Poly: how do I love thee?, Poly has many different descriptions, (1) First wonder of composition product, A description of po q, Example: differential equations, Another way to think about maps in Poly, Back to the coalgebra picture, Supplementary material
Mode dependent dynamical systems and polynomial functors
MIT, 2020-03-05
Outline (PDF)
Applied Category Theory: Towards a science of interdisciplinarity
ETH Zurich, 2019-09-25
Slides (PDF)
Keywords: A road to true interdisciplinarity, Our historical moment, Operad 1: wiring diagrams, Operad 3: probabilities, Functors translate between operads, W-algebra of tensor networks, Example wiring diagrams for named operations, What just happened?
Graphical abelian logic
ACT 2019, 2019-07-19
Slides (PDF)
Keywords: Graphical languages in category theory, Abelian categories, Why abelian categories are beloved, Some terms in the graphical language, The po-prop of abelian relations, Drawing functors PA->, (^-)A->is a lax monoidal po-functor, (^-) is bi-ajax and preserves involutions
Graphical abelian logic
CT 2019, 2019-07-11
Slides (PDF)
Keywords: Abelian categories, Why abelian categories are beloved, Introducing the po-prop of abelian relations, The po-prop of abelian relations, Finitely-generated abelian groups, (^-) is bi-ajax and preserves involutions, Aside: a sequence being a complex is its homology, Abelian calculi
Reglog -- the game
Compose Conference, 2019-06-24
Slides (PDF) | Video (YouTube)
Keywords: Minority Report, Compositionality, Regular logic and regular categories, Wiring diagrams as logical expressions, Regular calculi and regular categories, Common game platform, Game: Boolean circuits, Game: systems of linear equations
Monadic Decision Processes for Hierarchical Planning
MIT CT Seminar, 2019-05-23
Outline (PDF)
Applied Category Theory: Towards a science of interdisciplinarity
Oxford, Future of Humanity Institute, 2019-05-09
Slides (PDF)
Keywords: A road to true interdisciplinarity, Category theory as conceptual stem-cell, CT is the mathematics of mathematics., Compositionality: nestable arrangements, Operad 1: wiring diagrams, Operad 2: hierarchical protein materials, A zoo of operads: Grammars, The operad of sets
Applied Category Theory: Mathematics for Interdisciplinary systems modeling
MIT ASO, 2019-05-09
Slides (PDF)
Keywords: A road to true interdisciplinarity, CT is the mathematics of mathematics., Operads are everywhere, Operad 3: probabilities, Wiring diagram operads, similar to \#1, Multiple algebras for wiring diagrams operad, Equations and wiring diagrams, Application: smart grid
Applied Category Theory: Towards a science of interdisciplinarity
Bridgewater, 2019-05-09
Slides (PDF)
Keywords: A road to true interdisciplinarity, Popper's objection, Compositionality: nestable arrangements, Operad 2: another kind of wiring diagram, A zoo of operads: Grammars, Another theme of category theory, Category 2: sets and functions, The category of instances
Categorical Databases
Uber, 2019-04-22
Slides (PDF)
Keywords: A road to true interdisciplinarity, Our historical moment, Information kinematics, What is data transformation?, Categories = database schemas, Schema=Category, Instance=Set-valued functor, Example: The Grothendieck construction, CQL Capabilities
Reglog -- the game
MIT ACT Seminar, 2019-04-11
Slides (PDF)
Keywords: Minority Report, Adding beliefs, Let's hook it up, Mathematical specification of wiring diagrams, Regular calculi and regular categories, Common interface, Game: partitions puzzle (solution), A more complex example
Applied Category Theory: Towards a science of interdisciplinarity
UT Austin, 2019-03-11
Slides (PDF)
Keywords: A road to true interdisciplinarity, Our historical moment, Operad 1: wiring diagrams, Operad 3: probabilities, Wiring diagram operads, similar to \#1, Multiple algebras for wiring diagrams operad, Equations and wiring diagrams, Application: smart grid
Categorical Databases
Moderna, 2019-02-27
Slides (PDF)
Keywords: A road to true interdisciplinarity, Our historical moment, Information kinematics, What is data transformation?, Categories = database schemas, Schema=Category, Instance=Set-valued functor, Example: The Grothendieck construction, AQL Capabilities
Categorical Databases
Kensho, 2019-02-27
Slides (PDF)
Keywords: A road to true interdisciplinarity, Our historical moment, Information kinematics, What is data transformation?, Categories = database schemas, Schema=Category, Instance=Set-valued functor, Example: The Grothendieck construction, AQL Capabilities
Petri Banks, quiver representations, and control
MIT, 2019-01-10
Outline (PDF)
Categorical Databases
BAE Systems, 2019-01-09
Slides (PDF)
Keywords: A road to true interdisciplinarity, CT is the mathematics of mathematics., Information integration, The house-cat schema, Definition of a category I: Constituents, Functors: mappings between categories, Data transformations, Screenshot 1
Lenses: applications and generalizations
UC Riverside, 2019
Slides (PDF)
Keywords: An agent in an environment, The symmetric monoidal category of lenses, The agent-environment system, Hierarchical planning, What are bundles?, Interpretation of bimorphic lenses as trivial bundles, Ringed spaces, Lenses are everywhere?
Graphical calculus for abelian categories
MIT CT Seminar, 2019
Outline (PDF)
Lenses: applications and generalizations
MIT, 2019
Slides (PDF)
Keywords: An agent in an environment, Bringing lenses into the fold, Wiring diagrams, View update?, Pullbacks of bundles, How to think about, More principled view update, Formal properties of \lens_E
Graphical presentations of abelian categories
McGill University, 2019
Outline (PDF)
String diagrams for regular logic
Octoberfest, 2018-10-27
Slides (PDF)
Keywords: Minority Report, Picture proof, Comparing to other string diagram languages, Formal presentation of the calculus II., Regular hypergraph categories and regular categories, How to think of regular categories, Regular logic and cospan-algebras, Recalling the theorem
Some categorical perspectives on institutions
MIT, 2018-10-01
Outline (PDF)
Applied Category Theory: Towards a science of interdisciplinarity
Institute of Systems Research, UMD, 2018-09-28
Slides (PDF)
Keywords: A road to true interdisciplinarity, Our historical moment, Operad 1: wiring diagrams, Operad 3: probabilities, Wiring diagram operads, similar to \#1, Multiple algebras for wiring diagrams operad, Equations and wiring diagrams, Application: smart grid
Double categories
MIT Applied CT Seminar, 2018-08-23
Outline (PDF)
Decomposition spaces and toposes
MIT CT Seminar, 2018-07-19
Outline (PDF)
A topos-theoretic approach to systems and behavior
Category Theory Conference, 2018-07-09
Slides (PDF)
Keywords: An example system, NAS use-case as guide, An intervallic time-line,, Discrete vs.\ continuous time, Internal language of a topos, What is temporal type theory?, Local Dedekind numeric types, Setup
Backprop as Functor: A compositional perspective on supervised learning
Max Planck Institute, 2018-05-06
Outline (PDF)
A higher-order temporal logic for dynamical systems
Applied Category Theory Workshop, Lorentz Center, 2018-05-02
Slides (PDF) | Video (YouTube)
Keywords: An example system, Relations in a topos, First guess: the space R, and the upper half-plane, Our choice of topos, Dedekind numeric objects, Modalities in our setting, The problem: safe altitude
Discrete temporal type theory
MIT CT Seminar, 2018-04-26
Outline (PDF)
Categorical views of regular, coherent, geometric logic: from classical to wiring-theoretic
MIT, 2018-04-12
Outline (PDF)
Intuition/Talk on String diagrams for traced and compact categories are oriented 1-cobordisms
Toposes in Como, 2018-03-16
Outline (PDF)
A higher-order temporal logic for dynamical systems
NIST Applied Category Theory Workshop, 2018-03-16
Slides (PDF)
Keywords: An example system, A hypergraph category, NAS use-case as guide, First guess: the space R, Our choice of topos, The Kripke-Joyal semantics, Differential equations, Setup
A topos-theoretic approach to systems and behavior
CMU, 2018-03-16
Slides (PDF)
Keywords: An example system, NAS use-case as guide, An intervallic time-line,, Translation-invariant quotient topos, Preview of higher-order temporal logic for behavior, What is temporal type theory?, Local Dedekind numeric types, The problem: safe altitude
A higher-order temporal logic for dynamical systems
Barcelona, 2018-03-16
Slides (PDF)
Keywords: An example system, A hypergraph category, NAS use-case as guide, First guess: the space R, Our choice of topos, The Kripke-Joyal semantics, Differential equations, Setup
Metric realization of fuzzy simplicial sets
MIT Applied CT Seminar, 2018-02-22
Outline (PDF)
Backprop as Functor: A compositional perspective on supervised learning
Oxford OASIS, 2018-02-01
Outline (PDF)
Learning relations via adjunctions
MIT CT Seminar, 2018
Outline (PDF)
Some Applications of Category Theory
Salem State University, 2017-12-12
Slides (PDF)
Keywords: The need for organizational frameworks, What I mean by composition, Operad 1: WDs again, Operads and their algebras, Algebras for wiring diagrams operad, Relations are a W-algebra, A more complex example, Speed test: apples and oranges
A higher-order temporal logic for dynamical systems
AMS Fall Sectional, Riverside CA, 2017-11-04
Slides (PDF)
Keywords: An example system, Relations in a topos, First guess: the space R, and the upper half-plane, Our choice of topos, Dedekind numeric objects, Modalities in our setting, The problem: safe altitude
Cayley graphs and the Grothendieck construction
Harvard Math Table, 2017-10-24
Outline (PDF)
Category theory in science and engineering: A framework for information integration
MIT, 2017-10-02
Slides (PDF)
Keywords: Information integration, What I mean by composition, Operad 1: WDs again, Operads and their algebras, Multiple algebras for wiring diagrams operad, A more complex example, Speed test: apples and oranges, The PA idea is not particular to equations
Machine learning and category theory: perception and cognition
McGill Applied Mathematics Seminar, 2017-10-02
Slides (PDF)
Keywords: Applied category theory, Operad 1: wiring diagrams, What is an operad? An overview, Another look at matrix multiplication, Example wiring diagrams for named operations, Accuracy of the pixel array method 1in[width=1in]FinalButterflyEdited.png, The value of a mathematical language, Bifurcation diagrams are compositional
Using category theory for information integration
Caltech, AMBER Lab Seminar, 2017-10-02
Slides (PDF)
Keywords: Information integration, What I mean by composition, Operad 1: WDs again, Each operad has many algebras, Tensors are a W-algebra, Equations and wiring diagrams, Accuracy of the pixel array method 1in[width=1in]FinalButterflyEdited.png, Compositional mappings
Language and semantics for behavior
MIT CT Seminar, 2017-09-05
Outline (PDF)
The Pixel Array method for solving nonlinear systems
SIAM, 2017-07-13
Slides (PDF)
Keywords: Another look at matrix multiplication, A more complex example, So where are the limitations hiding?, Using array multiplication to solve systems, Multiplying Boolean matrices, Multiplying larger-order arrays, Example wiring diagrams for named operations, Apples and oranges
Compositional contracts for hybrid dynamical systems
SIAM, Novel Approaches for Systems of Systems, 2017-07-12
Slides (PDF)
Keywords: Systems and composition, Behaviors in the national airspace system, Example behavior types, ^X as a Heyting algebra, Examples of statements in the internal language, Modalities in general, Behavior contracts, Composing behavior contracts
An Operadic Approach to Compositionality
UAB Topology Seminar, Barcelona, 2017-06-12
Slides (PDF)
Keywords: Composition, Syntax and semantics, Example 2: hierarchical protein materials, String diagrams for monoids, Hypergraph categories, Example wiring diagrams for named operations, Discrete and continuous dynamical systems, Steady states are a compositional analysis
Sheaf-theoretic analysis of networked dynamical systems
Emerging Topics in Network Dynamical Systems, Lorentz Center, 2017-06-08
Slides (PDF)
Keywords: A behavioral and compositional approach, Interfaces, Behaviors on wires and in machines, What is a sheaf on a topological space X?, and predicates, Other semantics of wiring diagrams, Contracts are predicates on interfaces, Back to toposes again
Categorical databases
Broad Institute, 2017-03-29
Slides (PDF)
Keywords: Purpose of the talk, The basic similarity between databases and categories, Definition of a category I: Constituents, Foreign keys simply give functions, Changes in schema, Adjoints, Incorporating data types and functions, Relaxing into the RDF perspective
The pixel array method for solving non-linear systems of equations
MIT Mathematics IAP Lecture Series, 2017-01-30
Slides (PDF)
Keywords: What to expect from the talk, A more complex example, Using array multiplication to solve systems, Visual example again, Clustering as associative law, How to plot equations, Relation to dynamical systems and PDEs, Pixel Array analysis
Notes for LambdaConf
LambdaConf, 2017
Outline (PDF)
An Operadic Approach to Compositionality
Compositionality Workshop, Simons Institute for the Theory of Computing, 2016-12-05
Slides (PDF)
Keywords: Composition, Syntax and semantics, Example 2: hierarchical protein materials, String diagrams for monoids, Hypergraph categories, Example wiring diagrams for named operations, Discrete and continuous dynamical systems, Steady states are a compositional analysis
A whirlwind tour of category theory, for the working scientist and engineer
Telecom Bretagne, 2016-11-10
Slides (PDF)
Keywords: What is category theory?, Category theory at NIST, Functions, What more does arithmetic tell us?, Is this just a concept web?, The category of finite sets, Moving data along functors, Monoids
The Pixel Array method for nonlinear systems, and applications to numerical PDEs
Telecom Bretagne, 2016-11-10
Slides (PDF)
Keywords: What to expect from the talk, Selling points, Why and how does it work, Multiplying larger-order arrays, Clustering as associative law, Where false positives come from, Interconnected open dynamical systems (ODS's), Apples and oranges
The Pixel Array method for nonlinear systems, and applications to numerical PDEs
MIT Numerical Methods for PDE Seminar, 2016-10-26
Slides (PDF)
Keywords: What to expect from the talk, Selling points, Why and how does it work, Multiplying larger-order arrays, Clustering as associative law, Where false positives come from, Interconnected open dynamical systems (ODS's), Apples and oranges
A whirlwind tour of category theory, for the working scientist and engineer
Sandia National Labs, 2016-10-04
Slides (PDF)
Keywords: What is category theory?, Category theory at NIST, Functions, What more does arithmetic tell us?, Is this just a concept web?, The category of finite sets, Moving data along functors, Monoids
Air Force Research Laboratory, Dayton, 2016-06-29
Pixel matrices for big, messy, real-world data
5th Mini-Symposium on Computational Topology, SoCG, 2016-06-15
Outline (PDF)
Calculating steady states of nonlinear dynamical systems using matrix arithmetic
Binghamton University Mathematics Colloquium, 2016-04-07
Outline (PDF)
Operads as a potential foundation for systems of systems
Mathematical Biosciences Institute, The Ohio State University, 2016-03-22
Slides (PDF)
Keywords: What a foundation should provide, Feedforward composition style, Category Theory, Examples from computer science, Another example: dynamical systems, Discrete DS's also have this composition style, Changing the operad, Example
Bifurcation theory of networked dynamical systems
SIAM (did not occur), 2016
Outline (PDF)
A topos-theoretic approach to systems and behavior
Toposes in Como, 2016
Slides (PDF)
Keywords: An example system, NAS use-case as guide, An intervallic time-line,, Translation-invariant quotient topos, Preview of higher-order temporal logic for behavior, What is temporal type theory?, Local Dedekind numeric types, The problem: safe altitude
Category Theory 2016, 2016
Outline (PDF)
Operads: a mathematical approach to compositionality (Extended Abstract)
NIST Computational Category Theory Workshop, 2015-10-28
Outline (PDF)
Operadics: the mathematics of modular design
NIST, 2015-06-17
Slides (PDF)
Keywords: Materials design, Recipes, Applied category theory, Another way to see it, Operads and algebras = syntax and semantics, Sample architectures, What did operads really do for us?, Semantics of wiring diagrams
Protein materials architecture by design
NIST, 2015-06-16
Slides (PDF)
Keywords: Hierarchical protein materials in nature, Matriarch, Materials architecture, Demo, How operads are useful in design, Context-free grammars, A T-algebra of open dynamical systems, Modularity in nature
Operads as a language for modular design
FMCS 2015, 2015-06-05
Slides (PDF)
Keywords: A mathematical foundation is needed, Operads as a foundation for modularity, The operad of sets, The nomenclature we will use, The -algebra of stream processors, What's the relationship?, To begin: a concrete application, Matriarch as a design tool
Thinking about modularity in networks
University of Pennsylvania, Complex Systems Seminar, 2015-04-03
Slides (PDF)
Keywords: Motivation, It didn't quite work for everyone; why?, A picture of a recipe, An operad is an ``abstract modular environment", Example: composition of networks, We designed a tool called Matriarch, Materials architecture, Directed wiring diagrams are modular
A mathematical language for modular systems
AFOSR Program Review, 2015-01-29
Slides (PDF)
Keywords: Why a mathematical foundation is needed, Operads as a foundation for modularity, The operad of sets, The operad for monoids, The -algebra of stream processors, Traced categories, Where we are in the talk, Materials architecture
A category-theoretic approach to materials design
8th Design Theory SIG Paris Workshop, 2015-01-26
Slides (PDF)
Keywords: Informatics for design, High-level view of the talk, Example of materials architecture: collagen, Operad mappings, Structure and function: a dichotomy?, Computational modeling, Category theory was the software specification, Wiring diagrams 2: processes
A networked world
Workshop in Turin, 2015
Outline (PDF)
Category theory, the theory of mathematical structures: a whirlwind tour
MIT LIDS, 2015
Outline (PDF)
Notes on Applied category theory: Information structures and modular systems
Ecole Polytechnique Federale de Lausanne, 2015
Outline (PDF)
Category Theory -- A Formal and Flexible Interdisciplinary Language
Institute for Advanced Study, 2014-03-20
Outline (PDF)
Categorical databases
Amgen, 2014-03-04
Slides (PDF)
Keywords: Purpose of the talk, The basic similarity between databases and categories, Definition of a category I: Constituents, Foreign keys simply give functions, Changes in schema, Adjoints, Incorporating data types and functions, Relaxing into the RDF perspective
Categorical databases
PARC, 2014-03-03
Slides (PDF)
Keywords: Purpose of the talk, The basic similarity between databases and categories, Definition of a category I: Constituents, Foreign keys simply give functions, Changes in schema, Adjoints, Incorporating data types and functions, Relaxing into the RDF perspective
Categorical databases
Oracle, 2014-02-28
Slides (PDF)
Keywords: Purpose of the talk, You're not really using the relational model., The category of categories, Demo - People, Programming in FQL, Schema mappings and associated operations, Demo Example 2 in FQL IDE, FQL to RDF
Operads, and their algebras, for building new processors from old
UIUC, 2014-02-25
Outline (PDF)
Wiring diagrams and state machines
MIT, 2014-02-19
Slides (PDF)
Keywords: My goal: a visual, formal language for processes, Wiring diagrams, operad flavor: Many boxes inside, Tensor product of wiring diagrams, So... what to plug into these boxes?, Aside: Initialized machines act on lists, Checking on the composition XphiYpsiZ, Algorithmic state reduction, The math for baking in special symbols, part 1
Toward a categorical foundation of functional reactive programming
MIT, 2014-02-19
Slides (PDF)
Keywords: My goal: a visual, formal language for processes, Wires and boxes, Safe wiring diagrams, ^safe, Quick aside: how is x different than x?, Aside: Initialized propagators act on lists, Quick aside about safe WDs, State reduction, The math for baking in special symbols, part 1
Toward a categorical foundation of functional reactive programming
MIT, 2014-02-19
Slides (PDF)
Keywords: My goal: a visual, formal language for processes, Wires and boxes, Mathematical formulation of wiring diagrams, Quick aside: how is x different than x?, Motivation for state propagators, Example wiring diagram phiX-> Y, Algorithmic state reduction, The math for baking in special symbols, part 1
Toward a categorical foundation of functional reactive programming
MIT (PLV Lunch), 2014-02-19
Slides (PDF)
Keywords: My goal: a visual, formal language for processes, Tensor product of boxes, Example of a %(safe) wiring diagram (phi,phi^in,phi^out), is a symmetric monoidal category, Motivation for state propagators, An example of non-safe WDs, State reduction and wiring diagrams, A new monoidal category \bfW_
Toward a categorical foundation of functional reactive programming
Harvard University, 2014-02-19
Slides (PDF)
Keywords: My goal: a visual, formal language for processes, Tensor product of boxes, Unsafe wiring diagrams, Composing wiring diagrams, XphiYpsiZ, A questionable algebra, (phi)(X)(Y), (A) can always serve as state-set, Baking in special propagators
Categorical databases
Amgen, 2014-02-19
Slides (PDF)
Keywords: Purpose of the talk, The basic similarity between databases and categories, Definition of a category I: Constituents, Foreign keys simply give functions, Changes in schema, Adjoints, Incorporating data types and functions, Relaxing into the RDF perspective
Toward a categorical foundation of functional reactive programming
Carnegie Mellon University, 2014-01-23
Slides (PDF)
Keywords: My goal: a visual, formal language for processes, Tensor product of boxes, Unsafe wiring diagrams, Composing wiring diagrams, A questionable algebra, Example wiring diagram phiX-> Y, (A) can always serve as state-set, Baking in special propagators
Toward a mathematical science of informatics
National Institute of Standards and Technology, 2013-06-13
Slides (PDF)
Keywords: The goal is clarity and coherence, Category theory in mathematics, A database schema, from the CT viewpoint, Ologs connect natural language, databases, and categories, Ologs are database schemas 4: fiber product database, Relating different ologs, Functorial data migration for CT experts, Network of scientists 2: encoding interaction groups
Title: Lifting problems and data
MathFest, 2012-08-04
Slides (PDF)
Keywords: Research goal, What is a database?, Data columns as foreign keys, Schema=Category, Instance=Set-valued functor, Uses of functorial data migration 1: Translation F, Uses of functorial data migration 3: Joins via F, A different perspective on data, ``RDF", Global vs. local lifting criteria
Categorical ontologies and databases
Stanford Center for Biomedical Research, 2012-07-26
Slides (PDF)
Keywords: Research goal, A little history, Sets and functions, Data columns as foreign keys, Composing functors, Uses of functorial data migration 1: Translation F, Uses of functorial data migration 4: Unions via \Sigma_F, RDF schema and stores
A categorical approach to high-assurance science
Office of Naval Research, 2012-06-13
Slides (PDF)
Keywords: Science and map-making, Linked local charts = Atlas, What is needed from mathematics?, Definition of a category I: Constituents, Ologs are database schemas 2: database, Linking databases together, Uses of functorial data migration 2: Projection via \Delta_F, Category theory has 70 years worth of useful theorems
Categorical databases
Amgen, 2012-01-24
Slides (PDF)
Keywords: Purpose of the talk, The theory extends the reach of relational, The power of path equivalences, Foreign Keys and business rules, Composing functors, So many kinds of functors.., Incorporating data types and functions, Allowing for semi-structured data
Categorical databases
Johnson & Johnson, 2012-01-13
Slides (PDF)
Keywords: Purpose of the talk, The theory extends the reach of relational, A totally different category: an ordered set, Data columns as foreign keys, Changes in data, Adjoints, Incorporating data types and functions, Allowing for semi-structured data
Categorical databases
MIT, 2012-01-13
Slides (PDF)
Keywords: Purpose of the talk, The theory extends the reach of relational, A totally different category: an ordered set, Data columns as foreign keys, Changes in data, Adjoints, Incorporating data types and functions, Allowing for semi-structured data
Categorical databases
Special Geometry Seminar, UT Austin, 2012
Outline (PDF)
Categorical databases
Carnegie Mellon University, 2011-01-18
Slides (PDF)
Keywords: Purpose of the talk, What this viewpoint brings to databases, Functors to, Changes, How \Delta_F works, One more slide about views, RDF schema and stores, The nerve
Categorical Information Theory
MSS Colloquium, UIUC, 2011
Outline (PDF)
Categorical Information Theory
Topology Seminar, JHU, 2011
Outline (PDF)
Databases are categories
Harvard University, 2010-11-03
Slides (PDF)
Keywords: Purpose of the talk, What is a database?, What does this model do for you?, Allowing for semi-structured data, Interfacing between schemas, Provenance: a future history, Data columns as foreign keys, Relaxing into the RDF perspective
Databases are Categories II
Galois, 2010-10-22
Slides (PDF)
Keywords: Last time, Why venture into sketches?, Language of sketches as formal UML, Allowing for incomplete, non-atomic, or bad data, Views as polynomial functors, Bringing these concepts to researchers, How databases fit in, Example
Databases = Categories
MIT CSAIL, 2010-09-16
Slides (PDF)
Keywords: My background, Categories, Functors, Data migration 1: ``pull-back", The relational model, Data of a category, Examples of categories 3: Monoids, M-sets
Communication networks
MIT Linguistics, Semantics Reading Group, 2010-09-15
Outline (PDF)
Databases are Categories II
Galois, 2010-06-03
Slides (PDF)
Keywords: Last time, Why venture into sketches?, Language of sketches as formal UML, Allowing for incomplete, non-atomic, or bad data, Views as polynomial functors, Bringing these concepts to researchers, How databases fit in, Example
Topology and information
University of Chicago, 2010
Outline (PDF)
Mapping spaces in quasi-categories
University of Oregon, 2009-11-07
Slides (PDF)
Keywords: Homotopy everything, The model structure, Work with Dan Dugger, Definitions, Homotopy function complex, The Quillen equivalence, Solution: Weak Kan complexes, Mapping spaces