|Instructor:||Victor Reiner (You can call me "Vic").|
|Office: Vincent Hall 256, Telephone (with voice mail): 625-6682, E-mail: firstname.lastname@example.org|
|Classes:||Mon-Wed-Fri 2:30-3:20pm, Vincent Hall 1.|
|Office hours:|| Mondays and Wednesdays 11:15-12:05;
one can always arrange to meet me by appointment
An arrangement of hyperplanes is a finite collection
of codimension one subspaces in a vector space over some
field. Their study lies at the intersection of combinatorics,
topology, and geometry, as most enumerative, geometric or
topological questions about them reduce to combinatorics.
The answers to many of these questions have been
worked out, mostly in the last three decades.
Similarly, questions about arrangements of subspaces
(not necessarily of codimension one) are often controlled
by combinatorics, although here many more questions remain
In this course, we hope to explain the beautiful
combinatorial answers to many of these questions. Here are
some of the topics we'll think about covering:
|Prerequisites:||No absolute requirements. Of course a little bit of combinatorics would be useful. We will discuss some algebraic and topological things, so experience with algebra (like rings, modules) and algebraic topology (like fundamental groups, homology and cohomology) might be useful. But we'll try to review the basic facts about them anyway, often without proof.|
|Source materials, course requirements, and grading:||
We'll borrow heavily from the text
Arrangements of hyperplanes, P. Orlik and H. Terao, Springer-Verlag 1992
available from the bookstore, but is not absolutely required.
There is also a source list of papers, containing both useful surveys and other smaller papers in the subject.
There will be no homeworks or exams, but registered students are expected to attend, and must give one or two talks during the semester on papers chosen from the above source list, or any others proposed by the student that I approve. Students will be expected to meet with me at least once after I have approved their choice of paper to speak on, but before they give a talk, to discuss which aspects of the paper they will cover during the talk.