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Sylvain Poirier

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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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