PhD Student, University of Pennsylvania
Cellular sheaves are finite realizations of Sheaves, objects that have proven to be indispensable to the study of many branches of pure mathematics. At a high level, sheaves provide a means of extracting global characteristics of an object of interest from local data. The need to collate local data in a globally coherent way is abundant as well, and so it is hoped that cellular sheaves might become a broadly useful data structure in Applied Mathematics as well. Because of the strong finiteness conditions imposed on cellular sheaves, more can be said of them than of their more general counterparts. Propositions that are true of all sheaves can also be demonstrated by more elementary means with explicit constructions that are not available in the general setting. My research has focused on establishing the above facts by providing explicit proofs and constructions for what is known generally, and proving new things that are not generally true. I also work to solve basic problems of interest for someone interested in applications. In particular, my poster will mainly focus on an algorithm for generating random cellular sheaves, as their tightly constrained structure makes the task non-trivial.
Abstract: Category Theory is a well-known powerful mathematical modeling language with a wide area of applications in mathematics and computer science, including especially the semantical foundations of topics in software science and development. Categorical methods are already well established for the semantical foundation of type theory (cartesian closed categories), data type specification frameworks (institutions) and graph transformation (adhesive high level replacement categories). It is the intention of the ACCAT Workshops on Applied and Computational Category Theory to bring together leading researchers in these areas with those in software science and development in order to transfer categorical concepts and theories in both directions. The workshops aims to represent a forum for researchers and practitioners who are interested in an exchange of ideas, notions, and techniques for different applications of category theory. The seventh ACCAT workshop on Applied and Computational Category Theory 2012 was held in Tallinn, Estonia on the 1st of April 2012 as a satellite event of ETAPS 2012. This issue contains the full version of one of the invited talks as well as the submitted papers, which cover a wide range of applications of category theory, from model-driven engineering over transition systems in stochastic processes to transformations in M-adhesive categories.
Pub.: 21 Aug '12, Pinned: 29 Jun '17