{TALK
	   {"October 16}
           {"The higher Stasheff-Tamari posets and the higher Bruhat orders}
           {"Hugh Thomas}
           {"Fields Institute, University of Toronto}
	   {"hthomas@fields.utoronto.ca}
	   {"
The higher Bruhat orders are a generalization of weak Bruhat order on S_n.  
They can be defined combinatorially in terms of inversion sets,
generalizing the notion of inversion set of a permutation, or geometically
as sets of d-faces of an n-cube, generalizing the description of S_n as
paths through an n-cube.  The higher Stasheff-Tamari posets (which
generalize the Tamari lattices) have an analogous geometric definition
where the cube is replaced by a simplex.  In this talk, I will review all
the necessary definitions, and then discuss a new combinatorial "inversion
set" description of the higher Stasheff-Tamari posets which amounts to
giving from each Stasheff-Tamari poset into a corresponding higher Bruhat
order.
}
}