### MATH 5020: Topics in Algebra

**Description:** Advanced topics chosen from group theory, ring theory, number theory, Lie theory, combinatorics, commutative algebra, algebraic geometry, homological algebra, and representation theory. With change of content, this course may be repeated to a maximum of twelve credits.

**Prerequisites:** MATH 5211.

**Credits:** 3

### MATH 5020 - Section 1: Topics in Algebra: Cluster Algebras

**Description:** Cluster algebras are commutative algebras with a special combinatorial structure which are related to many different areas including Combinatorics, Representation Theory, Hyperbolic Geometry, Number Theory and Knot Theory. The subject is relatively young. The first paper on cluster algebras is published in 2002. Topics covered in the course include definition, examples, Laurent phenomenon and positivity, classifications, interpretation in terms of (1) triangulated surfaces, (2) representations of quivers, (3) perfect matchings of graphs, (4) continued fractions.

**Prerequisites:** MATH 5210

**Credits:** 3

**Sections: **Fall 2018 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

10510 | 5020 | 001 | Lecture | TuTh 12:30:00 PM-01:45:00 PM | MONT113 | Schiffler, Ralf |