Marius Furter

I am a third year PhD student in Mathematics, advised by Prof. Alberto Cattaneo at the University of Zurich. I am funded by the Digital Society Initiative Excellence Program Scholarship. I hold a Masters in Interdisciplinary Sciences (Biology and Chemistry) from ETH and a Bachelors in Mathematics from the University of Zurich.

My PhD aims at making probabilistic modeling and inference more widely accessible to scientists. This involves finding more intuitive and unified theoretical foundations, producing software tools that abstract away mathematical details, and writing clear exposition. Currently, I’m developing a framework for model building, inference, and experimental design for dynamic system biology models based on category theory and probabilistic programming.

I am also interested in monotone co-design. In 2025, I visited Gioele Zardini at MIT to incorporate probabilistic uncertainty into co-design. Before that, work with Jonathan Lorand resulted in a semester paper on modeling choice in co-design.

I enjoy teaching and creating math video lectures. You can find my teaching materials here.

news

Mar 24, 2025	Check out my new preprint “Composable Uncertainty in Symmetric Monoidal Categories for Design Problems” with Yujun Huang and Gioele Zardini.
Feb 01, 2025	Just returned from a 4-month visit with Giole Zardini at MIT. Will miss the people, but not the -10°C.

selected publications

Preprint

Composable Uncertainty in Symmetric Monoidal Categories for Design Problems

Marius Furter, Yujun Huang, and Gioele Zardini

Mar 2025

Abs DOI arXiv

Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging wires, or compact closed structures for feedback. A key example is the compact closed SMC of design problems (DP), which enables a compositional approach to co-design in engineering. However, in practice, the systems of interest may not be fully known. Recently, Markov categories have emerged as a powerful framework for modeling uncertain processes. In this work, we demonstrate how to integrate this perspective into the study of open systems while preserving consistency with the underlying SMC structure. To this end, we employ the change-of-base construction for enriched categories, replacing the morphisms of a symmetric monoidal V-category C with parametric maps A -> C(X,Y) in a Markov category induced by a symmetric monoidal monad. This results in a symmetric monoidal 2-category N*C with the same objects as C and reparametrization 2-cells. By choosing different monads, we capture various types of uncertainty. The category underlying C embeds into N*C via a strict symmetric monoidal functor, allowing (co)monoidal and compact closed structures to be transferred. Applied to DP, this construction leads to categories of practical relevance, such as parametrized design problems for optimization, and parametrized distributions of design problems for decision theory and Bayesian learning.