There is a very close relationship between the topology of a smooth manifold M and the critical points of a smooth function f on M. For example, if f is compact, then M must achieve a maximum and a minimum. Morse Theory is a far-reaching extension of this fact. Discrete Morse theory was a tool developed to study simplicial complexes(and cell-complexes), as opposed to smooth manifolds.

Rather than choosing a suitable class of continuous functions on our spaces to play the role of Morse functions, we will be assigning a single number to each cell of our complex, and all associated processes will be discrete. In this talk, we shall give an overview of this subject. Speaker(s): Malavika Mukundan (UM)