Sylvain Poirier

Thesis, articles and publications

I started my PhD thesis research in September 97 at Institut Fourier, Grenoble, with Christine Lescop  (http://www-fourier.ujf-grenoble.fr/lescop/homepage.html)
I worked on the Configuration space integral for links and tangles in R^4. I choosed the subject myself: after reading some articles in the domain of Vassiliev invariants, I imagined a construction that complemented other works dealing with the problem of comparing this integral with the Kontsevich integral. I first imagined it in terms of nonstandard analysis, but the reactions of other mathematicians lead me to search for a reformulation of this construction in terms of a compactification. I made it successfully, contributing to a better formalization of the construction of this integral formulated by other mathematicians and physicians on the subject, into a more rigourous approach.
My intoduction in French presented a "classical mechanics" version of the Chern-Simons gauge theory, whose quantum field version (seemingly the only one considered until now) was known as what gave the configuration space integral as a perturbation series.
My defence took place on January 28, 2000.

For the publication, I was asked to divide it again, and the revised first part (construction of the integral for links) is published in the AGT electronic Journal (in http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-40.abs.html) and put as a replacement of math.GT/0005085.
The referee had asked me to make some more developments to make the second part (extension to tangles as a parallel construction to the Kontsevich integral) more rigourous and readable. So it is a work that can be done in the future.

I also recently wrote an article which shows the three results announced in my thesis article (result of more precise rationality, criterion for the diagrams of nonempty image interior (now included in the revised version published above), cancellation of the anomaly in degree 5 using program maple).

You can find all this on my site, http://spoirier.lautre.net/thesis.html.

Now concerning my interest in more elementary mathematics, a version of an article in French entitled "Une nouvelle introduction à la physique mathématique" (="a new introduction to mathematical physics") has been published in "Lucrarile seminarului de creativitate matematica" vol.10, 2001, 175-195 (ISSN 1224-3310). But I have written much more material also in French and put it on my site (http://spoirier.lautre.net) without trying to publish it, because it aims to be the beginning of a future book.
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