Exceptionnellement à 15h.

Abstract: Feynman integrals, besides being useful in perturbative quantum field theories, are also a source of interesting transcendental functions such as multiple polylogarithms (or even more complicated and poorly understood classes of functions).  Still, at present we lack a good systematic way to compute these polylogarithmic functions.  One promising approach is through the study of singularities of these integrals.  Singularities of integrals of this type have been studied by Landau (in physics) and, independently, Leray (in mathematics).  We will adopt a perspective due to Pham (inspired by Thom), who described the singularities in terms of critical values of projection maps of so-called « on-shell spaces ».  These on-shell spaces are spaces where several propagators in the Feynman integrals become singular.  They have a natural description as configuration spaces of points with a rich geometry.  The degeneration loci of these configurations which are critical values for the projection maps above are directly relevant for physics, being used to build symbol entries for the symbol of polylogarithms in terms of which Feynman integrals can be computed.