The rook/pawn endgame class today was great. It was a little beyond my skill level calculation wise, but I was able to extract some really valuable concepts that I look forward to seeing in play, and which I think will be applicable beyond just r/p endgames as well.
My first takeaway was the relative value of pawns in the endgame -- exterior file pawns are weaker than interior file pawns. So, defending or exchanging, I should choose to preserve c-f file pawns over a/b and g/h file pawns. And attacking, I should try to get rid of my opponents pawns on those interior files.
Second, the importance of keeping the rooks as active as possible. Purely defensive moves may be necessary, but it's better to find positions that allow the rooks to attack as well as defend.
Third, I have this very vague set of ideas about things that I kept noticing during GM Magesh's analyses of the various positions we studied. The best moves usually were 1) central, 2) proximal to the goal, 3) space gainers or exploiters, and 4) connected or furthering connection. Every good move had one of these going on, and lots of them had two or three of these qualities. This is all is very fuzzy in my head still, and I have to think about it a lot more to figure out if it means something or is just a pattern that I'm seeing because humans are pattern seeking animals.
So boiled down, here's the list of what I learned to today.
Central is strong -- moves towards the center, pawns in the center, plans that use the center, controlling space in the center. Centricity is powerful, and if a plan or move doesn't further it, or weakens it, I should look for something better.
Proximity and connection. My pieces should be with reach of one another, and not forcibly seperated by space controlled by opponent - they should be connected. Moves should enhance my proximity and connection, or threaten my opponents. I shouldn't surrender proximity or connection without excellent compensation.
Space. Rooks need open ranks and files in order to work well. Avoid blocking them in in defensive positions. Conversely, make sure my king has sheltered spaces to move in - ideally, sheltered by pawns, allowing the rook the freedom to attack and defend the whole position, not just my king.