Science and Coktails

Have you ever looked closely at the world? How can the irregular structures that make it up be described effectively? In what ways do mathematics allow us to delve into the heart of these forms? How does randomness make it possible to generate such structures? Can the complexity of the real world be measured?

At first glance, the world seems easy to describe: regular shapes, smooth transitions, phenomena that could be modeled by smooth curves. But as soon as we look a little more closely, this apparent order begins to crack. Lines twist, patterns break apart, and irregularity takes over: the roughness of a landscape, the course of a river, air turbulence, the texture of an image, heartbeats, or the erratic movements of a financial market.

For a long time, classical mathematics proved poorly suited to describing this deeply irregular world. During the 20th century, new ideas emerged: fractals to capture irregularity, wavelets to analyze the local structure of a signal, and finally multifractal analysis to quantify the variability of this irregularity and to describe complexity itself.

This talk offers a gradual journey through these modern tools in order to understand how mathematics can shed light on the order hidden behind irregular phenomena.