Infinite-contrast homogenization : what and why?

I will present some personal ongoing research on infinite-contrast homogenization.

The first aim is to explain you some cool results and why they hold. That is not all, I also want to tell you about their genesis and the hidden part of the story. In the recent months and weeks, and under the pressure of external factors, the whole community of mathematicians started thinking about what it really means to be a professional mathematician. This is extraordinary, unprecedented, and maybe long due. Contributions are diverse, contradictory, sometimes naive, sometimes cynical, but they all have the merit to exist. Most of them place themselves at the level of the community (like the declaration of Leiden, the text signed by 25 Fields medalists, etc.), at the level of the human brain (have a look at the fantastic posts and book by David Bessis), and turned towards the future (either making predictions, suggesting directions, identifying risks, or proposing codes of conduct…). In hydrodynamic limits, the limiting equation does not give you much information on the microscopic states, this is the other way around, and we all are the microscopic states. We are humans who choose every single day what we are working on. To understand what a professional mathematician is, it also makes sense to observe mathematicians in their habitat, and identify what drives them to a problem and its solution, at the personal and human level. This is the second aim of this talk : share with you my current microscopic state on this math problem of my choice — I invite you to my habitat. This is very personal. I am willing to take the leap because I think it can be valuable (not because I am special, but because I am one particle among many), because the talk takes place in a friendly group, and because there is no right or wrong, this is just a measurement.