MATH 4810/5810, Graph Theory, Knots and their applications in Physics, Chemistry, and Engineering, August 2019

Instructor:

Dr. Markus Pflaum

Course Contents:

Graph and knot theory are two (related) mathematical disciplines with a fascinating history, deep results, and powerful applications in the sciences and engineering. Two highlights (among many) are Leonhard Euler′s solution of the Königsberg bridge problem, which is regarded as the first paper in graph theory, and the detection of a new knot polynomial by Vaughan Jones for which he was awarded the Fields medal in 1984. This course will first give an introduction into the necessary foundations in topology. We will then use these to study graphs and knots from a topological point of view. Several important results will be explained like the two mentioned ones or Kuratowksi′s criterion for the planarity of graphs. In the remainder we will study applications like molecular graphs, network graphs for electrical circuits, the description of DNA packing by knot invariants, knots in quantum field theory, and graphs in computer science and electrical engineering.

Course Announcement

Lecture Hours and Venue:

MTWThF 9:00 a.m. - 12:00 p.m., August 5 - 22, 2019.

Office Hours:

after class and by appointment

Course Project:

Each student has to write a short paper (around 5 pages) on a particular topic from Graph or Knot theory including their applications and give a 10min presentation on this in class. The papers are due August 22, 2019. A selection of possible topics is provided here, but you can propose your own project theme.

Homework:

Homework assignments will be given on the course webpage on a regular basis. Homework is usually due three to four days after the assignment. The homework will be discussed in class. Every student needs to present some homework problem.

Course Literature:

Titles of textbook(s) will be provided in time.