The Hodge Conjecture (Part 5)
Continuation of Part 4. Here I briefly discuss the connection between certain types of fluid flows (vector fields) and topology, which comes from Green's and Stokes' theorems and relates to work of de Rham and Hodge. In particular I emphasize the idea of local versus global concepts. If you want more depth on these issues look at the videos about Green's and Stokes' theorems in my "Multivariable Calculus" playlist, or for a more advanced version, watch my "Intro to Differential Forms" series.