# Jerusalem Mathematics Colloquium

Thursday, 3 June 1999, 4:00 pm

Mathematics Bldg., lecture hall 2

##

Isabella Novik

(The Hebrew University of Jerusalem)

"Upper Bound Theorems for simplicial manifolds"

** Abstract: **

Let \Delta be a (d-1)-dimensional simplicial manifold with
n vertices. One of the problems in combinatorics is: what is
the maximum possible number of i -dimensional faces of \Delta ?
What is the maximum possible Euler characteristic of \Delta ?

The Upper Bound Conjecture (UBC) asserts that if \Delta is
a Eulerian simplicial manifold then for any i the number of
i -dimensional faces of \Delta is not greater than the number
of i -faces of the cyclic d -polytope with n vertices.

In this talk we will outline the proof of the UBC for all
Eulerian manifolds. We also will sketch the proof
of the analog of the UBC for arbitrary (non-Eulerian)
simplicial manifolds and the (partial) proof of a conjecture
by K\"{u}hnel concerning the maximum Euler characteristic of
even-dimensional simplicial manifolds.

Coffee, Cookies, Company at the faculty lounge at 3:30.

List of talks, 1998-99

List of talks, 1997-98