Topological methods in singularity theory

Barnard College, New York NY

Investigators

Abstract

The project will provide travel support for US participants in a workshop ``Topological methods in singularity theory'' (http://www.icms.org.uk/workshops/topological) which will take place at the International Centre for Mathematical Sciences in Edinburgh, U.K., from 20--24 July 2015. Its purpose is to bring together specialists in singularity theory and topology from around the world, to have them present new developments and perspectives in singularity theory and new applications of topology to singularity theory, and to introduce these new directions to young researchers. Singularity theory studies mathematical phenomena associated with degenerations of generic objects into special ones and which results in radical changes of the objects. The study of such ``catastrophes" concerns a wide range of areas, ranging through economics, biology, chemistry, vision and medial imaging, control theory, to engineering and theoretical physics. Singularity theory and topology work with each other, and the collaboration has led to many rich connections with various fields such as mathematical physics, symplectic and contact topology, surgery theory. Recently, many new connections have appeared. For example, low dimensional topology and new homology theories have brought new invariants to singularity theory, there are new applications of surgery theory techniques, and applications of metric geometry also form a very fruitful new direction. The workshop will concentrate on five particular particular areas among which there have already been strong interactions: 1. Singularities, homology theories and related invariants, 2. Bilipschitz geometry of singular spaces, 3. Intersection homology, 4. Morse 2-functions, 5. Surgery theory.