Speaker
Description
A Reeb graph is a discrete invariant of a function on a space that provides information about the evolution of topology of the level sets. It is formed as the quotient of the space by contracting connected components of level sets of the function. Under sufficiently nice assumptions, e.g. for smooth functions on closed manifolds with finitely many critical values, it actually has the structure of a finite graph. Reeb graphs and their algorithmic version, mapper graphs, are widely used in computational topology, visualization and data analysis. In this talk we will discuss what information about the shape of space is encoded in Reeb graphs. In fact, there are only two necessary and sufficient conditions for a graph to be realized, up to homeomorphism, as the Reeb graph of a Morse function on a given manifold.
