Lawn Mowing and Shortcut Preventing: A minimal filling perspective on your garden’s design

As we all know, Gromov has two lawn-related pet peeves: everyone and their dog taking shortcuts on his lawn, and the excessively long time it takes to mow his lawn. Naturally, he’s been seeking the optimal lawn topography to mow as little as possible, while still ensuring no one takes any shortcuts through it. If you too have been struggling with these lawn-related complications, consider attending my talk (even if your lawn has genus greater than zero!). I will present a recent yet approachable development of the well know "I want a small lawn but please stop walking through by lawn, should it be a hemisphere?" conjecture.