James Fairbanks

Role

Principal Investigator

Program

Computational Science and Engineering

Degree

PhD

Status

Asst. Prof.

Lab member since

2021

James Fairbanks is an assistant professor in the department of Mechanical and Aerospace Engineering, and affiliated with the Institute for Computational Engineering, and the Florida Institute for National Security.

My research focuses on new paradigms in scientific computing, specifically applied category theory. This approach to mathematical modeling focuses on structure and structure preserving relationships between mathematical objects. The GATAS lab studies these topics and supports software-focused research in the AlgebraicJulia Ecosystem. We collaborate closely across the HWCOE and with external collaborators at NIST, AFRL, and the Topos Institute.

George Rauta

Program

CISE

Degree

PhD

Status

Starting

Lab member since

2022

George Rauta is a PhD student with a focus in numerical linear algebra and high-performance computing.

I believe that advances in the field of computer science are dependent on the existence of a highly performant computational foundation. It is critical that this foundation considers the theoretical aspects of algorithms, the method by which they are implemented in code and how they interact with the physical designs of modern processing and memory units.

I am also a developer on the Decapodes.jl and CombinatorialSpaces.jl projects.

Richard Samuelson

Degree

PhD

Status

Doctoral student

Lab member since

2024

Website GitHub

Richard Samuelson is a doctoral student researching category theory, convex analysis, and high-performance computing. He has made significant contributions to the CliqueTrees.jl package, implementing the ChordalLDLt multifrontal factorisation that underpins sparse symmetric positive-definite linear solves. These improvements accelerate nullspace and global-section computations in the CellularSheaves.jl library and enable more efficient compositional methods across the lab’s projects.

Selected publications

• Graphical Quadratic Algebra – ICTAC 2025 (Lecture Notes in Computer Science). Dario Stein, Fabio Zanasi, Robin Piedeleu, and Richard Samuelson. DOI: 10.1007/978-3-032-11176-0_18
• A Categorical Treatment of Open Linear Systems – Logical Methods in Computer Science, 2025. Dario Stein and Richard Samuelson. DOI: 10.46298/lmcs-21(3:11)2025

Joana Bou Barcelo

Program

MAE

Degree

PhD

Lab member since

2024

LinkedIn

Joana Bou Barcelo is a PhD student in the Department of Mechanical and Aerospace Engineering at the University of Florida, working at the boundary between the GATAS Lab’s compositional methods and nonlinear control.

Her work applies cellular sheaves to coordination problems in multi-agent systems. In Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves, written with Tyler Hanks, Cristian F. Nino, Austin Copeland, Warren Dixon, and James Fairbanks, the team poses the tracking of several unknown targets as a harmonic extension problem on a cellular sheaf. Because a sheaf can carry a different stalk over each agent, the formulation handles agents whose state spaces have different dimensions — the heterogeneity that makes these problems awkward to write down in the usual graph-Laplacian setting. The resulting decentralized controller is built from the sheaf Laplacian and comes with Lyapunov-based stability guarantees.

She presented this work as Heterogeneous Multi-Agent Multi-Target Tracking at the INFORMS Optimization Society Conference in Atlanta in March 2026.

Selected publications

• Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves. Tyler Hanks, Cristian F. Nino, Joana Bou Barcelo, Austin Copeland, Warren Dixon, James Fairbanks. To appear, IEEE. arXiv:2512.24886

Itay Kadosh

Program

MAE

Degree

PhD

Lab member since

2026

Google Scholar LinkedIn

Itay Kadosh is a PhD student in the Department of Mechanical and Aerospace Engineering at the University of Florida. His research interests are robotics, computer vision, and optimization.

Before joining UF he studied computer science and applied mathematics at the University of Texas at Dallas, where he worked in the Intelligent Robotics and Vision Lab on autonomous exploration and semantic mapping. That work built a robot that maps an indoor environment once and then keeps only the semantic object layer up to date on later visits, so it can track how objects move and change over time without remapping the geometry.

Selected publications

• Build Once, Monitor Continuously: Persistent Semantic Mapping via Autonomous Exploration and Open-Vocabulary Object Updates. Sai Haneesh Allu, Itay Kadosh, Tyler Summers, Yu Xiang. arXiv:2409.15493

Samuel Cohen

Status

Undergraduate researcher

Lab member since

2024

Samuel Cohen is an undergraduate studying math and computer science.

My work is implementing distributed optimization algorithms in the AlgebraicOptimization.jl package. This package uses the framework of category theory to exploit naturally occurring compositional structures in various optimization problems.

Matt Cuffaro

Role

Research Software Engineer

Status

Crushing it

Lab member since

2023

Matt Cuffaro is the systems administrator and research programmer for the GATAS lab.

I help my colleagues build the AlgebraicJulia ecosystem as well as be a custodian for our IT infrastructure.

Tyler Hanks

Program

CISE

Degree

PhD

Status

Graduated

Lab member since

2021

Tyler joined the GATAS Lab in the summer of 2021 as a graduate research assistant and has quickly become one of the group’s most visible contributors to the lab’s work at the intersection of optimization, control theory, and machine learning. His research is driven by a desire to make complex engineering problems easier to specify and solve by exploiting the compositional structures that naturally arise in multi-agent systems, distributed optimization, and deep neural-network architectures. To that end, Tyler applies tools from category theory, abstract algebra, and type theory, which are areas traditionally associated with pure mathematics, to create rigorous, modular frameworks that can be reused across disparate problem domains.

Beyond his theoretical work, Tyler has contributed substantial software infrastructure to the lab. He maintains the Julia-based codebase that implements the categorical abstractions used in the GATAS publications, and he routinely integrates those tools into the lab’s open-source repository, making them available to the broader scientific community.

In 2022 he was awarded a National Science Foundation Graduate Research Fellowship, a prestigious honor that supports early-career researchers as they start their academic journey. He presents his work at international conferences including American Control Conference, the Conference on Decision and Control, and Applied Category Theory. Tyler mentors undergraduate students including Sam Cohen and Trevor Gross and newer graduate students including Richard Samuelson. Through a combination of high-impact exemplifies the GATAS Lab’s mission to advance scientific computing by bridging abstract mathematics with concrete engineering applications. His hobbies include gaming, cycling, and playing music with his band Infinite Eights.

Selected publications

• Modeling Model Predictive Control: A Category-Theoretic Framework for Multistage Control Problems (2024). Tyler Hanks, Baike She, Evan Patterson, Matthew Hale, Matthew Klawonn, James Fairbanks. American Control Conference (ACC 2024). DOI: 10.48550/arXiv.2305.03820 (see ACC 2024 proceedings).
• Characterizing Compositionality of LQR from the Categorical Perspective (2023). Baike She, Tyler Hanks, James Fairbanks, Matthew Hale. IEEE Conference on Decision and Control (CDC 2023). DOI: 10.48550/arXiv.2305.01811 (see CDC 2023 proceedings).
• Compositional Exploration of Combinatorial Scientific Models (2022). K. Brown, Tyler Hanks, James Fairbanks. Applied Category Theory conference (ACT 2022). DOI: 10.48550/arXiv.2206.08755.
• Computational Category-Theoretic Rewriting (2022). K. Brown, Evan Patterson, Tyler Hanks, James Fairbanks. International Conference on Graph Transformation (ICGT 2022) – Best Paper Award. DOI: 10.48550/arXiv.2111.03784.

Tyler graduated in Spring 2026 and started a faculty position at the Florida Institute of Technology in Fall 2026!

Photos

Luke Morris

Program

CISE

Degree

PhD

Status

Graduated

Lab member since

2021

Website GitHub

Luke Morris is leading development on the CombinatorialSpaces.jl and Decapodes.jl projects, for representing multiphysics models and automatically generating simulations from those representations.

I am interested in problems that applied scientists face when they do any computational work. In particular, I mean the problems of developing models faster, and making the models themselves faster and more accurate. I lead a couple of projects on this front: Decapodes.jl and CombinatorialSpaces.jl.

We use techniques from Applied Category Theory (ACT) to represent models (as “Decapodes”) and how models compose together. These models are systems of partial differential equations (PDEs). ACT - the “science of composition” - lets us analyze scientific models as mathematical objects in their own right. Catlab.jl - an ACT programming library - enables us to write a library in an ACT-programming style, without sacrificing performance. We use Catlab’s implementation of “C-Sets” by specifying a small Decapode “schema”, which produces an efficient in-memory database to store a model. Doing algebra on these models then becomes as efficient as performing database operations. It is quite natural to interpret a system of PDEs as a relational database, adopting the point of view that such systems describe how physical quantities relate to one another.

Of course, when we generate simulations from these Decapodes, we need a framework for understanding numerical methods. Otherwise, we only have an encyclopaedia or ontology of physics equations, and nothing to “do” with them. The Discrete Exterior Calculus (DEC) is a good fit here, since it generalizes vector calculus, and differential operators become efficient matrix-vector operations that we can chain together. The DEC works on any type of manifold - a representation of space that makes sense, like a sphere, a plane, or a teapot - and so a Decapode is not necessarily tied to any particular shape or resolution of space. In 1 dimension, your physics make sense on a line or a circle. The CombinatorialSpaces.jl library is where we have implemented a representation of such spaces as “simplicial sets”, and definitions of differential operators.

Developing a library for scientific computing is best done by collaborating with the user that you have in mind. So I lead a few collaborations with labs who study space weather. One model simulates electron dissipation - where electrons end up in our atmosphere as they precipitate down from space - and another is a model for galactic cosmic ray (GCR) and solar energetic particle (SEP) transport

• how particles coming from other stars or the Sun travel through our solar system. There are applications for the weather on Earth as well, from modeling glacier dynamics to the circulation of matter in our atmosphere.

Photos

Trevor Gross

Status

Undergraduate researcher

Lab member since

2025

Website GitHub

Trevor Gross is an undergraduate junior studying computer science affiliated with the Florida Institute for National Security Talent Pipeline.

My research interests lie in developing and implementing new techniques to solve existing problems. I primarily work in the AlgebraicOptimization.jl library to improve the efficiency of distributed systems and make other engineers’ work easier. I am a highly motivated student who aims to contribute to research and industries worldwide.

Wilmer Leal

Role

Postdoctoral Fellow

Degree

PhD

Status

Writing

Lab member since

2022

LinkedIn

Wilmer Leal is a postdoctoral researcher at the Computer Science Department at the University of Florida, USA.

I am fascinated by the interplay between chemistry and mathematics, leveraging mathematical tools to solve chemical questions and using chemical intuition to inspire mathematical insights. My current research revolves around developing categorical models for various flavours of compositionality in chemistry. As a chemist, I am naturally inclined to reason and navigate through reaction networks, making hypernetworks a particularly exciting area of study for me.

Prior to joining the University of Florida, I pursued my Ph.D. in the Bioinformatics Group at the University of Leipzig and the Max Planck Institute for Mathematics in the Sciences, Germany. There, I explored both mathematical structures and vast chemical databases. This enabled me to delve into the depths of chemical space, uncovering its secrets and unraveling the intricate history of chemistry.

Ultimately, my goal is to advance our understanding of the rich interplay between chemistry, mathematics, computer science and history of science.

Photos

Benjamin Merlin Bumpus

Role

Research Assistant Professor

Degree

PhD

Status

Writing

Lab member since

2022

Website

Benjamin Merlin Bumpus was a faculty research scientist and led the algorithms subproject within the GATAS Lab.

In 2023 he accepted a professorship at the Institute of Mathematics, Statistics, and Computer Science (IME) at the University of São Paulo (USP) in Brazil, where he now heads the CombTheta research group and the CUÍCA (Categorical Understanding in Computation and Algorithms) lab. His move to USP has expanded his collaborative network across South America and Europe, resulting in joint projects on categorical methods in computational complexity and graph theory. Recent highlights including the Brazilian Category Theory Conference and our paper on temporal data with sheaves being published.

Ben’s research focuses on the emergence of complexity and its relationship to compositionality—the principle that the structure or meaning of a whole depends on that of its parts. He investigates computational complexity, combinatorial explosion, and their connections to graph structure theory, parameterized complexity, and finite model theory, using category theory to relate and generalize tools across these areas.

Ben introduced sheaf theory to the GATAS Lab, initially motivated by characterizing fixed-parameter tractable algorithms and dynamic programming categorically. This work deepened the group’s understanding of local-to-global alignment in compositional computation, extending the earlier focus on how monoidal functors interact with colimits.

Photos

Patrick Stokes

Program

CISE

Degree

PhD

Status

Qualifying

Lab member since

2021

Patrick Stokes was a faculty research scientist in the GATAS lab.

My background is in signal processing, statistical modeling, and system identification in computational neuroscience. My research interest is applying category theory to develop structures and algorithms for robust inference and identification of complex, high-dimensional, multi-scale, and stochastic systems.

Taylor Frederick

Taylor Frederick is a research scientist who likes math.

Decapodes

Decapodes.jl is a graphical tool for the composition of physical systems. This library includes tooling which takes advantage of the formalization of physical theories described by DEC provided by CombinatorialSpaces.jl.

Links:

• Diagrammatic Equations Paper
• Decapodes Computational Paper
• Code
• Docs

Project team

Photo	Name	Member since	Degree	Program
	Luke Morris	2021	PhD	CISE
	Matt Cuffaro	2023	—	Research Software Engineer
	George Rauta	2022	PhD	CISE

Project articles

Subproject: general categorical equations

Project Leader: Kevin Carlson at the Topos Institute

• Topos Blog 1
• Topos Blog 2
• arXiv

Sponsors

Decapodes has been supported by the following DARPA programs:

• Automating Scientific Knowledge Extraction
• Directly Computable Models
• Automating Scientific Knowledge Extraction and Modeling

Algebraic Dynamics, Optimization, and Control

AlgebraicControl.jl

Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. We present a novel Julia library that leverages our theoretical results to automate the implementation of correct-by-construction MPC problems in software.

Project team

Photo	Name	Member since	Degree	Program
	Tyler Hanks	2021	PhD	CISE
	Samuel Cohen	2024	—	—
	Richard Samuelson	2024	PhD	—

Project articles

Sponsors

AlgebraicOptimization and Control has been supported by the following programs:

• NSF: Graduate Research Fellowship Program
• ONR: Domain Transfer for Continuity of Performance
• AFRL: Griffis Summer Internship Program

Compositional Algorithms with Sheaves

StructuredDecompositions.jl

Project team

Photo	Name	Member since	Degree	Program
	Benjamin Merlin Bumpus	2022	PhD	Research Assistant Professor
	Wilmer Leal	2022	PhD	Postdoctoral Fellow

Project articles

Sponsors

Computational sheaf theory has been supported by the DARPA program Automating Scientific Knowledge Extraction and Modeling.

Decapodes: A diagrammatic tool for representing, composing, and computing spatialized partial differential equations

Abstract

We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations, a method for composing systems of partial differential equations using an operad of wiring diagrams, and an algorithm for deriving solvers using hypergraphs and string diagrams. The string diagrams are in turn compiled into executable programs using the techniques of categorical data migration, graph traversal, and the discrete exterior calculus. The generated solvers produce numerical solutions consistent with state-of-the-art open source tools as demonstrated by benchmark comparisons with SU2. These numerical experiments demonstrate the feasibility of this approach to multiphysics simulation and identify areas requiring further development.

Links

• Journal
• Code
• Docs

A diagrammatic view of differential equations in physics

Abstract

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm mathematical footing, while also systematizing a broadly applicable framework to reason formally about systems of equations and their solutions. Our main mathematical tools are category-theoretic diagrams, which are well known, and morphisms between diagrams, which have been less appreciated. As an application of the diagrammatic framework, we show how complex, multiphysical systems can be modularly constructed from basic physical principles. A wealth of examples, drawn from electromagnetism, transport phenomena, fluid mechanics, and other fields, is included.

Links

• Topos Blog 1
• Topos Blog 2
• Journal
• PDF
• Code
• Docs

A Diagrammatic Presentation of Equations in Categories

Abstract

Lifts of categorical diagrams D:𝖩→𝖷 against discrete opfibrations π:𝖤→𝖷 can be interpreted as presenting solutions to systems of equations. With this interpretation in mind, it is natural to ask if there is a notion of equivalence of diagrams D≃D′ that precisely captures the idea of the two diagrams “having the same solutions”. We give such a definition, and then show how the localisation of the category of diagrams in 𝖷 along such equivalences is isomorphic to the localisation of the slice category 𝖢𝖺𝗍/𝖷 along the class of initial functors. Finally, we extend this result to the 2-categorical setting, proving the analogous statement for any locally presentable 2-category in place of 𝖢𝖺𝗍.

Links

• Topos Blog 1
• Topos Blog 2
• arXiv
• Code
• Docs

Bibliography Table

This is the same bibliography data as the publications list, collapsed into a single sortable table. Click a column header to sort; use the box to filter.

Defense Advanced Research Projects Agency

DARPA has supported the GATAS Lab and the AlgebraicJulia Ecosystem through the following projects.

1. Automating Scientific Knowledge Extraction
2. Directly Computable Models
3. DARPA Young Faculty Award
4. DARPA Young Faculty Award: Director’s Fellowship
5. Automating Scientific Knowledge Extraction and Modeling

Sponsor website

Office of Naval Research

ONR has supported the GATAS Lab and the AlgebraicJulia Ecosystem through the following projects.

• Domain Transfer for Continuity of Performance Across Synthetic Aperture Sonar
• Extracting, Explaining, and Estimating Information in Sonar Data (E3ISD)
• Mine Counter-measures Situational Awareness
• Performance Estimation of Underwater Mine Counter-measures Operations

Sponsor website

Air Force Research Laboratory

AFRL has supported the GATAS Lab and the AlgebraicJulia Ecosystem through the following projects.

• Summer Internships through the AFRL Scholars Program
• Summer Internships through the Griffis Scholars Program
• Collaboration with AFRL research staff

Sponsor website

National Science Foundation

NSF has supported the GATAS Lab and the AlgebraicJulia Ecosystem through the following projects.

• NSF Graduate Research Fellowship Program: Tyler Hanks

Sponsor website

Call for Participation

The Eighth International Conference on Applied Category Theory will take place at the University of Florida on June 2-6, 2025. The conference will be preceded by the Adjoint School on May 26-30, 2025. This conference follows previous events at Oxford (2024, 2019), University of Maryland (2023), Strathclyde (2022), Cambridge (2021), MIT (2020), and Leiden (2019).

Applied category theory is important to a growing community of researchers who study computer science, logic, engineering, physics, biology, chemistry, social science, systems, linguistics and other subjects using category-theoretic tools. The background and experience of our members is as varied as the systems being studied. The goal of the Applied Category Theory conference series is to bring researchers together, strengthen the applied category theory community, disseminate the latest results, and facilitate further development of the field.

Important dates

All deadlines are AoE (Anywhere on Earth).

• February 26: Title and brief abstract submission
• March 3: Paper submission
• April 7: Notification of authors
• May 19: Pre-proceedings ready versions
• June 2-6: Conference

Submissions

The submission URL is: https://easychair.org/conferences/?conf=act2025

We accept submissions in English of original research papers, talks about work accepted/submitted/published elsewhere, and demonstrations of relevant software. Accepted original research papers will be published in a proceedings volume. The conference will include an industry showcase event and community meeting. We particularly encourage people from underrepresented groups to submit their work and the organizers are committed to non-discrimination, equity, and inclusion.

• Conference Papers should present original, high-quality work in the style of a computer science conference paper (up to 12 pages, not counting the bibliography; more detailed parts of proofs may be included in an appendix for the convenience of the reviewers). Such submissions should not be an abridged version of an existing journal article although pre-submission arXiv preprints are permitted. These submissions will be adjudicated for both a talk and publication in the conference proceedings.

• Talk proposals not to be published in the proceedings, e.g. about work accepted/submitted/published elsewhere, should be submitted as abstracts, one or two pages long. Authors are encouraged to include links to any full versions of their papers, preprints or manuscripts. The purpose of the abstract is to provide a basis for determining the topics and quality of the anticipated presentation.

• Software demonstration proposals should also be submitted as abstracts, one or two pages. The purpose of the abstract is to provide the program committee with enough information to assess the content of the demonstration.

The selected conference papers will be published in a volume of Proceedings. Authors are advised to use EPTCS style; files are available at style.eptcs.org.

Reviewing will be single-blind, and we are not making public the reviews, reviewer names, the discussions nor the list of under-review submissions. This is the same as previous instances of ACT.

In order to give our reviewers enough time to bid on submissions, we ask for a title and brief abstract of your submission by February 26. The full two-page pdf extended abstract submissions and up to 12 page proceedings submissions are both due by the submissions deadline of March 3 11:59pm AoE (Anywhere on Earth).

Please contact the Programme Committee Chairs for more information: Amar Hadzihasanovic (amar.hadzihasanovic@taltech.ee) and JS Lemay (js.lemay@mq.edu.au).

Programme Committee

See conference website for full list: https://gataslab.org/act2025

• PC Chairs

  • Amar Hadzihasanovic (PC Chair), Tallinn University of Technology
  • JS Lemay (PC Chair), Macquarie University

• PC Members

  • Benedikt Ahrens, Delft University of Technology
  • Robert Booth, University of Edinburgh
  • Cameron Calk, Laboratoire d’Informatique et Systèmes (LIS)
  • Cole Comfort, Université de Lorraine
  • Valeria de Paiva, Topos Institute
  • Elena Di Lavore, Oxford University
  • Martin Frankland, University of Regina
  • Jonas Frey, Laboratoire d’Informatique de Paris-Nord (LIPN)
  • Tobias Fritz, University of Innsbruck
  • Zeinab Galal, University of Bologna
  • Léonard Guetta, Utrecht University
  • Robin Kaarsgaard, University of Southern Denmark
  • Martti Karvonen, University College London
  • Shin-Ya Katsumata, Kyoto Sangyo University
  • Alex Kavvos, University of Bristol
  • Kohei Kishida, University of Illinois Urbana-Champagne
  • Gabriele Lobbia, Università di Bologna
  • Fosco Loregian, Tallinn University of Technology
  • Giulio Manzonetto, L’Institut de Recherche en Informatique Fondamentale (IRIF)
  • Dan Marsden, University of Nottingham
  • Adrian Miranda, University of Manchester
  • Koko Muroya, National Institute of Informatics
  • Nina Otter, Université Paris-Saclay
  • Hugo Paquet, Institut national de recherche en sciences et technologies du numérique (INRIA), Paris
  • John Power, Macquarie University
  • Dorette Pronk, Dalhousie University
  • Callum Reader, University of Sheffield
  • Martina Rovelli, University of Massachusetts Amherst
  • Mehrnoosh Sadrzadeh, University College London
  • Peter Selinger, Dalhousie University
  • David Sprunger, University of Indiana
  • Alex Toumi, PlantingSpace
  • Todd Trimble, Western Connecticut State University
  • Sean Tull, Quantinuum
  • Paul Wilson, Hellas.AI
  • Dusko Pavlovic, University of Hawaii
  • Ruben Van Belle, University of Oxford
  • Priyaa Varshinee Srinivasan, Tallinn University of Technology
  • Gioele Zardini, Massachusettes Institute of Technology