Call for 2026 Summer Research Associates
Come spend the summer at the Topos Institute! For early-career researchers, we’re excited to open up applications for our 2026 Summer Research Associate program.
Postdoctoral Researcher (Alum)
Xiaoyan Li is a computer scientist and mathematical modeller with expertise spanning computer science, data science, and applied mathematics. She holds a Bachelor’s degree in Applied Mathematics, as well as Master’s degrees in Computer Science and Petroleum Engineering. She is currently a Ph.D. candidate in Computer Science at the University of Saskatchewan, scheduled to defend her dissertation in March 2025.
Her research lies at the intersection of machine learning, dynamical system modeling, and applied category theory, with a strong focus on real-world applications. On the application side, her work focuses on developing theory-based machine learning models for public health, enabling policy-making through infectious disease transmission simulations, forecasting, and counterfactual interventions. On the theoretical side, she explores applied category theory for dynamical systems, aiming to design next-generation, modular, and composable modelling frameworks and tools.
Today we’re excited to announce the first alpha release of CatColab 0.2: Wren. CatColab is software for making models of the world together.
Today we’re excited to announce the first pre-alpha release of our new software CatColab 0.1: Hummingbird. CatColab is software for making models of the world together.
In the third post of this series about Relational Thinking: from abstractions to applications, we look at the story-telling approach that we took in writing the book.
In the second post of this series about Relational Thinking: from abstractions to applications, we look at the technologies used to build the book.
In the first post of this series, we introduce the freely available online book Relational Thinking: from abstractions to applications, starting with the story of how it came into being and giving a brief overview of its contents.

A follow-up to Algebraic Geometry for the Working Programmer, this post explains a category-theoretic approach to symbolic open dynamical systems.