SISSA Geometry Seminars

[Ugo Bruzzo]

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SISSA GEOMETRY SEMINARS
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Prof. Letterio Gatto from Politecnico
di Torino will give a talk on

Schubert Calculus on a Grassmann Algebra

on Wednesday, March 21, at 12:00 noon in Room B
(basement, SISSA Main Building).

Abstract:  I will report on some joint work with
T. Santiago. There is a natural derivation on the
exterior algebra of a finite free module over a
graded ring of characteristic zero which
describes, in a unified fashion, different kinds
of Schubert Calculus on grassmannian varieties 
(classical,  small quantum, or equivariant).
Pieri's and Giambelli's formulas are recovered,
respectively, from Leibniz's rule and integration
by parts  holding for such a derivation. As an
example we offer an explicit set of Pieri's
formulas for the equivariant cohomology of the
grassmanninan G(k,n)  under a certain torus action
having isolated fixed locus, studied  by Knutson
and Tao via puzzles, in Duke Math. J. 119, no. 2,
2003, p. 221--260), thus giving a simple answer to a
question raised by Lakshmibai, Raghavan and Sankaran
in Pure Appl. Math. Q. 2 (2006), no. 3, 699--717.

      U. Bruzzo