# Jerusalem Mathematics Colloquium

Thursday, 29th January 2009, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Eran Nevo

(Cornell)

"On the g-conjecture"

** Abstract: **

In 1970 McMullen conjectured a complete characterization of the
possible face-vectors of boundary complexes of simplicial polytopes.
These numerical conditions were proved in 1980, necessity by Stanley
and sufficiency by Billera and Lee, known as the g-theorem.
The proof of necessity shows that a hard-Lefschetz decomposition holds
for an appropriate ring associated with the polytope. A major open
problem, known as the g-conjecture, is to extend these numerical and
algebraic assertions to the larger family of simplicial sphere, and
beyond.

This problem illustrates interesting relations (some are only
conjectured) between combinatorics, commutative algebra, algebraic
topology and geometry.
We will describe these relations and indicate recent developments on
the g-conjecture.

Some of the new results are joint work with Eric Babson, some are
joint work with Martina Kubitzke.

Light refreshments will be served in the faculty lounge at 3:30.

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