Program

Algebraic topology provides measures for global qualitative features of geometric and combinatorial objects that are stable under deformations, and relatively insensitive to local details. This makes topology into a useful tool for understanding qualitative geometric and combinatorial questions. Considerable momentum has developed in recent years towards applications of algebraic topology in various contexts related to data analysis, object recognition, discrete and computational geometry, combinatorics, algorithms, and distributed computing. The MSRI program will gather the workers in these areas for concentrated interactions, and will make a strong effort to communicate the nature of these developments to the more general mathematical public. In addition, there will be tutorials in the early phase of the program on background in topology as well as the relationships between the methods of topology and statistics. We expect that the program will make a substantial contribution to establishing future research directions in the area. The program will focus on (1) the topology of point cloud data and (2) topological methods in combinatorics and computer science. The study of point cloud data will include work on high dimensional data sets coming from the analysis of images, from neuroscience, from the study of phylogenetic trees, and from shape and feature recognition. In the direction of combinatorics and computer science, we will include work on graph coloring, lower bounds for complexity of computational tasks, discrete and computational geometry, and distributed/concurrent computing. The figure above shows a cubical version of the Boy surface (an immersed projective plane with a single triple point). It is from the paper by A. Schwartz & G. M. Ziegler in Experimental Math. 13 (2004), 385-413. If interested in this program, please apply on line at www.mathjobs.org. For further information on applications, go to http://www.msri.org/applications/. Those applying for a postdoctoral fellowship at the Fields Institute in connection with the Spring Thematic Program on Geometric Applications of Homotopy Theory should so indicate in their applications. There may be a limited number of joint appointments, to be held at MSRI in Fall 2006 and at Fields in Winter 2007.