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Some Applications of Duality Between Polynomials and
                         Formal Series
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Bernard Mourrain

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Date:  July 19th (Friday)\\
Time: 14:00-14:25\\

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Abstract
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We are going to describe a duality between the algebra of polynomials
and the algebra of formal series, viewed as a space of differential
operators. This duality is connected to the notion of inverse systems
introduced by Macaulay (1916). We will recall the main properties of
these inverse systems and see how difficult operation on ideals become
easier with formalism. Then we will focus on 0-dimensional ideals and
show how the local ring of an isolated point can be computed by
{\it integration} in the dual space. We will give some applications to the
computation of local residues in the case of complete intersection, to
the analysis of real branches of locally complete intersection case.
We will end by some computations of global residues, where formal
series appear explicitly. Some connections with Grobner bases
computations will also be illustrated.

