Liverpool Centre for Mathematics in Healthcare

Lectures - Generalized power diagrams, balanced k-means, and the representation of polycrystals: Professor Peter Gritzmann (Technische Universität, München)


Time: Tuesday February 18, 14:00 - 15:00

Title: Generalized power diagrams, balanced k-means, and the representation of polycrystals

Venue: Proudman Lecture Theatre (MATH-027)

Abstract: Based on a discrete convex maximization model we give an efficient algorithm for computing feasible generalized power diagrams with near-optimal separation properties. Further, we show how this approach can be used to generalize the classical k-means algorithms from data analysis so that it becomes capable of handling weighted point sets and prescribed lower and upper bounds on the cluster sizes; the above discussion being based on joint work with S. Borgwardt and A. Brieden. 

We also indicate how to handle the discrete inverse problem from material science to compute grain maps, i.e., representations of polycrystals, based only on measured data on the volume, center and, possibly, moments of their grains; this part of the discussion being work jointly undertaken with A. Alpers, A. Brieden, A. Lyckegaard and H. Poulsen. 


Biography: Professor Peter Gritzmann is a distinguished German mathematician whose interest lies in the areas of discrete mathematics, optimisation and applied geometry. He is currently a professor of Mathematics at the Technical University of Munich, where he has served as Vice President for Administration and was director of the Carl Linde Academy. He has held visiting positions at the University of Washington (Seattle), the University of Minnesota (Minneapolis) and the University of Paris VII.

From 1974 to 1978 he was a fellow of the Studienstiftung des Deutschen Volkes and 1986/87 he had a Fedor Lynen Research Fellowship from the Alexander von Humboldt Foundation. He has also presided over the Alexander von Humboldt Foundation committee for scholarships.

In 1992 he was awarded the Max Planck Research Award; in 2000, the Karl Max von Bauernfeind Medal; and in 2013 the Euro Excellence in Practice Award. In 2002 and 2003 he served as president of the German Mathematical Society.