A Mathematical Zoom on an Irregular World
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.
Talk by
Céline Esser
Céline Esser is a mathematician and professor in the Department of Mathematics at the University of Liège. After completing her PhD there, which she defended in 2015, she went on to pursue her research at the Paul Painlevé Laboratory at the University of Lille, where she immersed herself in the study of random models. She later returned to Liège, where she was appointed professor in 2020. She now teaches there (mainly analysis and probability theory) and carries out her research within a small team consisting of one postdoctoral researcher and two PhD students.
Her research lies at the intersection of wavelet theory, multifractal analysis, and stochastic analysis. She is particularly interested in studying and characterizing irregular functions, quantifying their roughness, and understanding the structure of random processes.
In addition to her research and teaching activities, she devotes part of her work to the dissemination of mathematics. She is notably co-coordinator of the Math.en.JEANS project for the Wallonia-Brussels Federation and an active member of the Belgian Mathematical Society.
