|Maths and me (interview)|
A personal homepage is also made to introduce yourself, isn't it?
Would you like to interview me?
[You] Mr Darnière, tell us about your maths.
[Me] Oh, gosh! It isn't that simple...
[You] OK, what do you do actually?
[Me] Well, my speciality is the study of rings which satisfy a local-global principle like Hasse's principle: it is tempting to reduce the theory of such a ring to the theories of its fibers (the rings in which local points take place) plus some additionnal information such as the topology of its maximal spectrum or the absolute Galois group of its fraction field. Of course this is not possible in general, but under reasonable assumptions one can prove some embedding theorems which give rise to a classification of those rings from which decidability and model-completeness results can be derived as well as (sometimes) applications to algebra.
[You] Is all that stuff really mathematics?
[Me] Undoubtly. More precisely it is model theory.
[You] Model... what!?
[Me] I have build an introductive HTML page I called "Qu'est-ce que la théorie des modèles ?" (in french, sorry) where I have tried to answer this question. It is supposed to be (and I hope it is) readable by an undergraduate student (apart from some exemples). I recommand you to have a look on it.
[You] How did you eventually come to this?
[Me] By following Krivine's course in Jussieu, called "logic and foundations of computer science". Then I did a PhD in mathematics. My thesis entitles "Étude modèle-théorique d'anneaux satisfaisant un principe de Hasse non singulier", or in universally understood language "Model theoretic study of rings satisfying a non singular Hasse principle". If you are interested in this topic, you can download it as well as all my recent (pre-)prints
[You] And where is it possible to obtain more information about mathematical logic?
[Me] Er... you can go for exemple to the web site of the Mathematical Logic Team in Jussieu, or visit Mathematical Logic around the world, a page which collects numerous links.
[You] Thank you, Mr Darniere.
[Me] You're welcome, thancks to you.