Equivariant Cohomology and the Pattern Map

Billey and Braden defined a geometric pattern map on flag 
manifolds which extends the generalized pattern map of 
Billey and Postnikov on Weyl groups.   The interaction of 
this torus equivariant map with the Bruhat order and its 
action on line bundles lead to formulas for its pullback 
on the equivariant cohomology ring and on equivariant 
K-theory.   These formulas are in terms of the Borel 
presentation, the basis of Schubert classes, and 
localization at torus fixed points. This is joint work 
with Praise Adeyemo of the University of Ibadan in Nigeria.