MA591 Section 005 -- Spring 2015 -- Cluster Algebras

Lecture schedule

MWThF 10:15-11:05am 2111 BU

Offices and office hours

My office is in 3208 SAS, I am there most of the days from around 9am to 8pm; feel free to stop by for any question you may have. If you do not want to risk me not being available drop me an e-mail and we can set up a meeting time.


Grades in this course will be based mainly on student presentations to be held at the end of the semester.

During classes I will also assign problems for you to consider. Some of these will be straightforward computations, some will require some thought and some might be research questions.


Good preparation in undergraduate mathematics (linear algebra, abstract algebra, analysis).

List of the topics covered in class

Lecture Date Topic
1 01/07 Examples
2 01/09 Total positivity
3 01/16 Grassmanians
4 01/21 Matrix mutations
5 01/23 Cluster algebras of geometric type
6 01/26 Exampled revised
7 01/28 Cluster algebras
8 01/30 Semifields
9 02/02 Proof of Laurent phenomenon I
10 02/04 Proof of Laurent phenomenon II
11 02/06 Upper/Lower bounds amd upper cluster algebras
12 02/09 d-vectors I
13 02/11 d-vectors II
14 02/13 Dynkin diagrams
15 02/16 Finite type classification
16 02/18 Improvvisation on homeworks
17 02/20 Growth rates
18 02/25 Almost-positive roots
19 03/02 Generalized associahedron
20 03/04 Exchange relations
21 03/06 Surfaces I
22 03/16 Surfaces II
23 03/18 Surfaces III
24 03/23 Principal coefficients
25 03/25 Ecxhange graphs
26 03/27 F-polynomials, c-vectors
27 03/30 g-vectors
28 04/01 Dualities
29 04/06 Quivers
30 04/08 Gabriel's theorem
31 04/10 CC map
32 04/13 Seminars
33 04/15 Seminars
34 04/17 Seminars

My lecture notes

Here is a copy of the notes I use during class. Beware of mistakes, errors and messy handwriting.
Lectures 1-10
Lectures 11-17
Lecture 18
Lecture 19
Lecture 20
Lecture 21
Lecture 22
Lecture 23
Lecture 24
Lecture 25
Lecture 26
Lecture 27
Lecture 28
Lecture 29
Lecture 30
Lecture 31

The usual fine prints


Attendance is mandatory and will be checked daily. If you miss class or are late, you are still responsible for all material covered and assignments due. Make up tests will be given only with excused absences. The university attendance policy can be found here.

Academic Integrity

I assume that anything turned in with your name on it is your own work. Each time you submit a test, quiz, or homework assignment, you affirm the honor pledge, "I have neither received unauthorized aid nor given aid on this assignment." The minimum penalty for cheating is a grade of zero on the assignment; violators may be reported to the Academic Integrity Review Board, which can impose additional sanctions. The code of student conduct can be found here.

Disability Services

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1), a copy of which can be found here
Last modified: Thursday, 28-Aug-2014 18:42:26 EDT