This series of talks was part of the Algorithmic Spectral Graph Theory Boot Camp. Videos for each talk are available through the links above.
Graphs are ubiquitous in all modern sciences. This motivates a need for algorithmic tools that are capable of analyzing and computing on graphs in an efficient manner. A need that is even more pressing now that the graphs we are dealing with tend to be massive, rendering traditional methods no longer adequate.
In this talk, I will discuss a recent progress on the maximum flow problem and use it as an illustration of a broader emerging theme in graph algorithms that employs optimization methods as an algorithmic bridge between our combinatorial and spectral understanding of graphs.
I will also briefly outline how this line of work brings a new perspective on some of the core continuous optimization primitives - most notably, interior-point methods.