# Seminars at the Faculty of Informatics

### The On-Line Heilbronn's Triangle Problem in Three and Higher Dimensions

The Faculty of Informatics is pleased to announce a seminar given by Gill Barequet

DATE: Thursday, November 21st 2013
PLACE: USI Lugano Campus, room A34, Red building (Via G. Buffi 13)
TIME: 15.30

ABSTRACT:
In this talk I will show a lower bound for the on-line version of Heilbronn's triangle problem in three dimensions.  Specifically, I will provide an incremental construction for positioning any number of points in the 3-dimensional unit cube, so that if it stops after the $n$th point, every tetrahedron defined by four of these points has volume $\Omega (\frac{1}{n^{3.333...}})$.
I will will also discuss generalizations to higher dimensions.

BIO:
Gill Barequet is currently an Associate Professor and head of the Center for Graphics and Geometric Computing at the Department of Computer Science of the Technion (Israel Institute of Technology) in Haifa, Israel.
He received his B.Sc. in Mathematics and Computer Science, and M.Sc.
and Ph.D. in Computer Science from Tel Aviv University in 1985, 1987, and 1994, respectively.
He later had a post-doctoral position at Johns Hopkins University in 1996-98, and a visiting position at Tufts University in 2009-10.
In 2009 he won the Henri Taub Prize for academic excellence.
His research interests include discrete and computational geometry, combinatorics, interpolation and reconstruction algorithms, and geometric applications in CAD, medical imaging, and molecular biology.
He holds five US patents in related areas.