Colloquium
4:00 p.m., Monday (Jan. 27th)
Math 203
Kalle Karu
Harvard University
On rational and nonrational polytopes
Let P be a polytope and f_i the number of idimensional
faces of P. An interesting problem in combinatorics is to
decide what conditions the numbers f_i must satisfy. This
problem has a beautiful connection with algebraic geometry
(due to R. Stanley). To a polytope P with rational vertices
one can associate an algebraic variety. Then familiar conditions
on the cohomology of the variety define conditions on the face
numbers f_i. In this talk I discuss Stanley's proof of the
rational case and its extension to the case of a nonrational
polytope.
Refreshments will be served at 3:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
