The University of Michigan Combinatorics Seminar
The title refers to two seemingly unrelated open combinatorial
conjectures from the late 1980's/early 1990's. The Charney-Davis
Conjecture asserts an inequality on face numbers of certain simplicial
spheres. The Neggers-Stanley Conjecture asserts that certain generating
functions (counting linear extensions of a poset by number of descents)
have only real zeroes.