During my summer research ( Report ), I focused on formalizing the Max-Plus Spectral Theorem.

I initially used this tropical algebra framework to optimize scheduling and spot bottlenecks for the Equissima equestrian triathlon (Poster | Application) . But the beauty of mathematical modeling is that the same math can be applied almost anywhere.

Curious to see how this scales to a much larger system, I decided to look at one of the densest and most precise networks in the world: the Swiss railways.

Recently, I had the privilege of riding in the control cabin with a train driver on Lausanne's R1 line. Watching the operations firsthand allowed me to see the real-world delays, track synchronizations, and tight schedules that dictate railway traffic.

By mapping the physical constraints of the train's progression into a weighted directed graph, we can theoretically apply the Max-Plus eigenvalue λ to predict network bottlenecks with O(1) complexity (code). Even more importantly, watching the human side, how the driver anticipates and reacts to signals, me things that pure theory simply misses.

Stepping out of the lab reminded me why I love formalizing mathematics: beyond abstract rigor, it gives us the tools to build reliable foundations for the infrastructure we use every day.

A huge thank you to the railway staff for welcoming me aboard and helping me bridge the gap between pure math and real-world logistics!

taught