Today was the HRUMC XIII. I met Ken Ono. I also gave a talk about eliminating "monsters" (i.e. curves that obviously wouldn't be minimizing) with elementary reasoning. It went quite well, and it was much better than when I practiced yesterday, due to my giving the motivation behind why we would want to eliminate monsters in the first place. Here was my talk:
TITLE: Isoperimetric Regions in Sectors of the Gauss Plane: Eliminating MonstersNext year I am writing a thesis with Professor Adams. His research is in knots and hyperbolic 3-manifolds, and as you may recall, he is teaching my tiling tutorial next semester. Since I don't know about 3-manifolds, I'll probably do either knots or tiling. My particular question is still very much up in the air.
Diana Davis, Williams College
ABSTRACT: The cheapest way to enclose area in the Euclidean plane is by a circle, but what if the plane has varying density? What if we only consider a pie-shaped sector of the plane with varying density? I`ll show how to eliminate shapes (such as the circle) that we now know cannot be minimizing, and give conjectures and evidence for the best shape.