Event Type:

Department Colloquium

Date/Time:

Wednesday, November 10, 2004 - 08:00

Location:

Gilkey 104 (<b> NOTE: unusual day, time, and location </b>)

Guest Speaker:

Dusan Repovs

Institution:

University of Ljubljana

Abstract:

We shall begin the talk with a short historical account of the life and work of Eduard Helly, including his years spent in a labor camp in Siberia and his long trek home across Japan and Egypt. In the sequel we shall discuss his famous theorem on intersections of convex sets and its topological version. We shall present recent joint work with U.H. Karimov, which resulted in an unusual twist of events. First, we have shown that a statement in a paper by Molnar from 1950's, strongly related to the Topological Helly Theorem, is in fact, false. (In the meantime, Molnar's assertion has been used since then in several papers by other authors, some quite recently.) Second, and more important, after the observation by Bogatyi few years ago that there is in fact, no complete proof of the Topological Helly Theorem, we found a proof of the special case of this theorem (the general case being still open) which we shall outline in the talk. We shall also discuss related problems and conjectures.