Harvard University Computer Science Colloquium Series 33 Oxford St.,Cambridge, MA 02138 Colloquium Computing the Shape of a Space Afra Zomorodian Computer Science Department Dartmouth College http://www.cs.dartmouth.edu/~afra/ Thursday, February 1, 2006 4:00PM Maxwell Dworkin G125 (Ice Cream at 3:30PM - Maxwell Dworkin 2nd Floor Lounge Area) Abstract For any problem, we can identify a space within which the solution lies. The shape of this space is critical in whether we succeed in finding the solution. Most disciplines take a quantitative approach, analyzing the geometry of the solution space. However, the topology of the space - how it is connected - impacts the effectiveness of the resulting geometric algorithms. Such topological questions have given rise to the area of computational topology. In this talk, I discuss persistence homology, a computational approach to discovering the connectivity of a space. Persistence reveals the underlying algebraic structure of a multi-scale view of a sampled space. I begin by motivating the approach through examples from computer graphics. After describing the theory, I present applications in biophysics and analysis of natural images. Finally, I motivate the need for multidimensional persistence and give a brief overview of a recent theoretical result. Host: Professor Steven Gortler _______________________________________________ Colloquium mailing list Colloquium(a)deas.harvard.edu https://lists.deas.harvard.edu/mailman/listinfo/colloquium _______________________________________________ iic-seminars mailing list iic-seminars(a)calists.harvard.edu http://calists.harvard.edu/mailman/listinfo/iic-seminars