2. Michael Molloy et al.'s 1998 paper on the mixing rate of the triangulation walk on convex polygons. Because I'll also present the proof in Thursday's lunch meeting, I'll only cover those details that I can't go into during the earlier meeting.
3. My proof of the connectedness of the triangulation graph of arbitrary planar point set, and the degree lower bound. The connectedness proof is a simplified version of Kai Jin and Xiaohui Bei's.