Abstract:

Morse Theory explores the interplay between topology and analysis. For

example, a natural question is how the shape of a space affects the behavior

of functions (measurements) defined on a space. Conversely, what can the

output of a function (measurement) tell you about the shape of the space. I

will describe how the topology of a space puts non-obvious restrictions on

the behavior of functions and, in turn, how a space can be built up from

knowing the behavior of a function on it.