The Alexandrov-Fenchel inequality, a fundamental result in convex
geometry, has recently been shown to be one component within a broader
'Kahler package'. This structure was observed to emerge in different
areas of mathematics, including geometry, algebra, and combinatorics,
and encompasses Poincare duality, the hard Lefschetz theorem, and the
Hodge-Riemann relations. After unpacking these statements within the
context of this talk, I will explain where complex geometry intersects
with convex geometry in the proofs.
Based on joint work with Andreas Bernig and Jan Kotrbaty.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/3050