Algebraic algorithms for Cell Complexes: Incubation Activity

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

DMS-0138323 Reinhard C. Laubenbacher This award supports research concerned with the algorithmic representation of cell complexes, a special type of topological space. These complexes arise as topological models of data and processes in science and engineering. Specific applications of interest are to biological, social, and communications networks, as well as to problems in statistics. Topological invariants of the complexes provide measures of certain characteristics of the processes producing the data. The use of cell complexes as data models represents a new application of these structures to science and engineering network problems. The methods employed include tools from computational algebra, combinatorics, and combinatorial topology, thereby making a contribution to the applicability of new mathematical areas to some pressing and challenging applied problems. Research results will be disseminated directly to the end user outside the mathematical community. The project impacts a number of graduate students, including students from underrepresented groups.