Applied Topology Unit (Dmitry Feichtner-Kozlov)
Algebraic Topology is a classical branch of mathematics. Its origins are combinatorial, based on triangulations of topological spaces. In the later developments major algebraization of the subject has taken place, leading to the introduction of many algebraic invariants as we know them today.
Recent years have witnessed an explosive growth in the use of methods from Algebraic Topology in other fields of mathematics, exact sciences, and computer science. This led to the emergence of the new field Applied Topology, which remains the main focus of the research of this unit. We are interested both in developing the formal theory, as well as in applying it outside of the field, for example to Theoretical Distributed Computing.
A major research direction is applying Algebraic Topology to the questions in Discrete Mathematics, leading to the subject of Combinatorial Algebraic Topology.