Problems

Background: 

We assume that participants have taken an undergraduate linear algebra course and are familiar with the very basics of graph theory. It would be helpful (but not necessary) for participants to have Sage installed on their computer. Beyond that, here are some texts that we’ll draw from:

• Lecture 1 of Reiner’s notes on “Lectures on Matroids and Oriented Matroids”

• Chapter 7 of Ardila’s “Algebraic and geometric methods in enumerative combinatorics"

• the introduction to Ziegler’s “Lectures on Polytopes”

• Chapter 3 of Beck—Robins' “Computing the Continuous Discretely”

Description of the problem and some background can be found here.

Suggested Reading:

• Masaki Kashiwara, in D-modules and Microlocal Calculus (Translations of Math Monographs, AMS)

• Janos Kollar, in arXiv:alg-geom/9601026

• Dragan Milicic in https://www.math.utah.edu/~milicic/Eprints/dmodules.pdf

• Uli Walther, in Compositio Math. (141), 2005

• Uli Waltherand Anton Leykin, in Math. Sci. Res. Inst. Publ., 67 on the special year in commutative algebra and noncommutative algebraic geometry 2012/13 

It would be helpful to have some familiarity with the following 

• Danilov-Karzanov-Koshevoy triangulation of a flow polytope or 

• multitriangulations of a polygon

• other sorts of “noncrossing” things 

• simplicial complexes

• some ideas pertaining to Hibi rings, but this shouldn't be too relevant