Let me warn you, I am not known for my brevity.
This project would not have been possible without my project advisor, Ethan
Bloch, who provided incalculable expertise, energy, cheerfulness, and boundless en-
thusiasm, even when I started talking about graph theory. His meticulous and un-
tiring attention to detail and careful craftsmanship, expressed as ominous and inde-
structible spider webs of red ink, was absolutely invaluable and very nearly painless,
and was never expressed without the deepest kindness. This project would also not
have been possible without my other project advisor, Lauren Rose, who was the
Frst mathematician I ever worked with at Bard, and whose passion, experience,
knowledge, and skill taught me as much by example as by explicit instruction. Both
of them have my eternal and deepest gratitude.
I owe a great deal to the entire extended mathematics department family, in-
cluding Ethan and Lauren, but also Mark Halsey, Robert McGrail, Ranny Bledsoe,
Rebecca Thomas, Sven Anderson, Robert Cutler, and Matthew Deady, who each
provided a di±erent viewpoint into this wacky world of mathematics, but who have
one and all demonstrated to me an inspiring passion for their subjects.
Mark, thank you for showing me that mathematicians are fully capable of being
almost preternaturally serene and calm, unbelievably organized, and still supremely
enthusiastic and, well, great. Bob, thank you for showing me some of the most
fascinating and beautiful mathematics I have ever seen, which I probably would not
have seen but for you.
rReiner from the University of Minnesota
and Professor Robin ²orman from Rice University, for being nice enough to meet
with us and talk about Laplacians, and for pointing me in the right direction.