Intersection cohomology and cd-index of fans
-- Kalle Karu

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For a projective toric variety X corresponding to a
    simplicial fan F, the singular cohomology of X can be
    used very effectively to understand the combinatorics
    of F.  When the fan F is not simplicial, there are two
    better behaving replacements for singular cohomology:
    intersection cohomology and cd-index.  The two theories,
    despite having different origins -- the first in geometry
    and the second in combinatorics -- are actually close
    cousins.  In this talk I will explain the similarities
    between them and some parallel results that hold in both
    theories.