Leonardo Dias
I’m Leo, a Brazilian engineering student at École Polytechnique. I’m interested in the meeting point between applied mathematics and computation—from machine learning and formal verification to electronics.
I keep this site as a record of what I’m learning, building, and thinking about, with the occasional detour into music.
Recent writing
All notes →- ↗
From fixed points to ODE solutions: Banach’s idea
How Banach's fixed-point theorem explains Picard's method of successive approximations and the Cauchy–Lipschitz theorem.
Ordinary Differential EquationsAnalysisFixed-Point Theory
Projects
All projects →Coffio
A Wi-Fi controller that turns a conventional coffee maker into a programmable connected appliance.
CompleteGenetic PID Tuning
A controlled comparison between genetic search and the Ziegler–Nichols rule for tuning a PID controller.
CompleteClassical vs. Learned Image Segmentation
A controlled comparison of GrabCut and a lightweight U-Net on binary semantic segmentation.
CompleteFiducial Marker Tracking for UAVs
A YOLOv8 detector coupled to a Kalman filter to maintain a landing-marker estimate through intermittent visual detections.