Graduate school teaches you how to take a big problem and break it down into bite-size pieces. Building a research program involves that aspect (especially in training students to do research). But a research program also requires the reverse: seeing how to go from small problems to the generalizations that create a coherent research program. What are the necessary ingredients for doing so? It's like anything else you make grow: you go inch by inch, and row by row - until you make your garden grow.* I will describe the process of taking highly concrete, tightly focused problems and expanding them into medium-sized research programs, explaining what's needed for such generalizing to lead to healthy, valuable research directions.
* From "The Garden Song" by David Mallet.