Goodwill hunting problems

The movie "Good will hunting" features some nice problems in graph theory and for linear algebra. Here is an exhibit from 2003 with handout[PDF]. A low resolution clip had been included in 2006 in the math in movie collection here and here. After working a bit on Bowen-Lanford zeta functions Mathtable talk [PDF] the clip got mentioned also in the paper. There are various reasons, why I like these problems. First of all, it features the Bowen-Lanford Zeta function, named after Oscar Lanford III, who was my PhD advisor. These Bowen-Lanford Zeta functions appeared naturally in the context of connection calculus, which is part of Quantum calculus. Indeed, and that only emerged on Block island is that the Green function values, the diagonal entries of (L-z)-1xx can be expressed then in terms of the Euler characteristic of the unit sphere in the graph. Very exciting. Here is the clip showing the two problems:

M4V, Ogg Webm. imdb link, Update August 10, 2022: Since recent paper of mine on eigenvalues [PDF] of the Kirchhoff matrix deals with quivers, I looked a bit at the literature of Good Will hunting. Here is an article from 2013, explaining a bit more about the math. There is also quite a bit of math in the book ``Math goes to the movies" from 2012. Compare also my handout from 2003[PDF] I have used the movie clip as an illustration in the classroom already in the course Math 21b in 2001, when teaching linear algebra. I must say that my linear algebra teacher Ernst Specker whom I had for two semesters in linear algebra during freshmen year has used graph theory in his course (like computing eigenvalues or eigenvectors). Such problems appeared for example in homework.

Oliver Knill, Posted January 5, 2017,