Would you tell us about your works and what you will be talking about at ICIAM?
The major part of my current research, in collaboration with Thierry Bodineau of the École Polytechnique, Laure Saint-Raymond and Sergio Simonella of the École Normale Supérieure de Lyon, is related to "Hilbert's sixth problem", as stated by David Hilbert at the second International Congress for Mathematicians in Paris in 1900. The question is to understand and justify the different levels of description that can be made of a fluid (typically water, or a gas such as the atmosphere), from its microscopic to its macroscopic description: to what extent are those descriptions of the same physical object, whose equations are so different, actually reconcilable?
What does it mean to you to be a mathematician? What is it you like in the job?
Mathematics is a field where curiosity and imagination play an essential role and where freedom is considerable. Doing mathematics or research in general implies accepting to make mistakes, spend hours implementing unsuccessful ideas and come up from time to time with something new, which may be considered as interesting and sometimes even beautiful.
What I like about the job is also the absence of hierarchy between colleagues (at least most often!): from the moment you start a doctorate, you are part of the mathematical community.
What are the benefits of collaborative work?
There are several types of collaborations. Those, occasional, born from a coffee discussion or at a workshop, when you realize that the result you are looking for may be obtained by combining your knowledge and techniques with your colleagues’. And others, which can last for years if not throughout your career, where the scientific unfolding is running on the long-term and sometimes along unexpected lines. The latter collaborations, very enriching mathematically, also sustain rich human relationships. When you work in collaboration with others, you also benefit from the others’ optimism when your own confidence fails, and vice versa… I very much like working in small groups of two or three people, exchanging ideas and knowing that one good idea usually comes up after a dozen bad ones!
How do you situate your work in relation to applied and industrial mathematics?
My mathematical work has no industrial purpose. As for applications to other scientific disciplines, the mathematics I do, without leading to immediate applications, most often have a strong link to physics because of the models studied or the questions raised. To me there is no clear boundary between the so-called applied and the so-called fundamental mathematics, so my guess is, my work probably lies somewhere at the interface between the two!
Isabelle Gallagher is a Professor at Université Paris Diderot & École Normale Supérieure de Paris and a member of the Département de mathématiques et applications (DMA) (CNRS & ENS Paris).
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