Geometric Harmony and Balance: Chopping up space with centroids.

September 5, Olin 201, 4pm. We'll talk about the last several years of this student/faculty research project. Recently, some of this work was published in Mathematics Magazine with two student authors (Katie Gillespie and Sophie Kotok) and was even featured on the cover. Centroidal Voronoi tessellations (CVTs) occur in nature, for example in fish spawning, they also occur in applications from image compression to resource allocation. We'll explain what a CVT is through a series of diagrams. We'll talk about some of the questions we've answered and the many questions that remain open. The content is geometric in nature and should be accessible to anyone with mathematical curiosity. 

 

 

 

A Voronoi tessellation (VT) starts with a collection of points in the plane and divides the plane into regions about each point so that when you are in a point's region you are closer to that point than you are to any other region's point. A CVT is a special VT in which the points happen to also be the centroids of their regions. This extra constraint imposes a rich structure on the regions and invites interesting geometric questions.

BIO: Albert Schueller is a professor of mathematics at Whitman College. He has published a few papers on CVTs--two of them jointly with Whitman students. He has always tried to work on mathematics that has applications and is accessible to Whitman students. He is also interested in programming, game design, machine learning and inverse problems.