This lecture begins with a problem involving unfolding and refolding. Examples of smooth foldings and unfoldings are given, followed by a problem involving the wrapping of a sphere and a proof that the wrappings are contractive.

This lecture presents the hydrophobicity (HP) model for protein folding and optimization using parity cases. Interlocked 3D chains are presented through a table depicting different cases for combinations of open and closed chains.

This lecture begins with how to construct a gluing tree. Combinatorial bounds and algorithms are proved for gluing results, which include the general case, edge-to-edge, and bounded sharpness. The different gluings for the cross are also shown.