Class meets at: Goldsmith 117, MW 4:05pm - 5:25pm.
Lecturer: Theo Douvropoulos (you can call me "Theo")
Office Hours: Tuesdays 3-4pm and Wednesdays 11-noon at Goldsmith 204. Also virtually on Thursdays 10:00am-11:00am at the link https://brandeis.zoom.us/j/2242246971.
Wednesday 8/28 | Introductions; Sage and Jupyter; Hyperplane arrangements and the characteristic polynomial.
Wednesday 9/4 | Zaslavsky's theorem
Monday 9/9 | Graphical Arrangements
Wednesday 9/11 | Graphical Arrangements
Monday 9/16 | Intrinsic volumes interpretation of the characteristic polynomial
The material this day is recent and is not covered in a textbook. The five references are either research notes or papers; in each one of them I have marked 2-4 pages where we see two new interpretations of the characteristic polynomial. Study this material in the order I indicate following my notes.
Wednesday 9/18 | More on Intrinsic Volumes, Internal and External angles of Cones
Monday 9/23 | Posets as Cones in the Braid Arrangement
Wednesday 9/25 | Order polynomials and linear extensions of posets
Monday 9/30 | Eulerian polynomials; Carlitz and Worpitzky identities; and a useful change-of-basis
Wednesday 10/2 | P-partitions; order polynomials on posets via descents of their linear extensions
Monday 10/7 | Fans, complete fans, complete fans of posets
Wednesday 10/9 | Cambrian trees and Cambrian fans: Project description
Take-home midterm 10/14-10/18