Instructor: Damir Yeliussizov [damir at math ucla edu]
Lectures: MWF 3-3:50 pm, Geology 4645
Office hours: M 4-5 pm, MS 5346
The topic will be Algebraic Graph Theory. This course will cover an introduction to spectral graph theory and various related topics from algebra and algebraic/enumerative combinatorics.<!br> <!br>
- A. E. Brouwer, W. H. Haemers, Spectra of Graphs, Springer, 2012 (available here)
- B. Bollobás, Modern Graph Theory, Springer, 1999
- R. P. Stanley, Algebraic combinatorics, Springer, 2013 (available here)
Grading will be based on several problem sets. Collaboration is allowed but solutions should be written individually and not copied from anywhere.<!br> <!br>
Tentative list of topics:
- Spectral graph theory. Graph eigenvalues. Enumeration of walks. Matrix-Tree theorem. Connectivity and cuts. Random walks.
- Rings with polynomial identities via graphs. Amitsur-Levitski theorem. Weyl algebra. Capelli identities. Grassmann algebra.
- Eulerian tours. Enumeration in directed and undirected case, orientations. Interlace polynomials.
- Gessel-Viennot method. Determinants and Pfaffians.
- Tableaux, dual graphs, and symmetric functions.
- Introduction to Total Positivity.