Speaker: Francisco Santos

Title: 50 years of the Hirsch conjecture

The Hirsch conjecture was stated in 1957 in a letter from Warren M.  
Hirsch
to George Dantzig. It states that the graph of a $d$-polytope with $n$  
facets
cannot have diameter greater than $n - d$.

Despite being one of the most fundamental, basic and old problems in
polytope theory, what we know is quite scarce. Most notably, no  
polynomial
upper bound is known for the diameters of polytopes. In contrast, very  
few polytopes
are known where the bound $n-d$ is attained (basically one, apart from  
trivial examples
and polytopes constructed from it). In this talk we will have a look  
at the conjecture
focusing on "partial counterexamples".