**The photo:** A street in Budapest.

- Notes from a class by Harm Derksen: homepage here
- Notes from lectures by Bill Crawley-Boevey: Part I and Part II
- Notes from a class by Henning Krause: here

- Jan. 13: Introduction to the course

(lecture notes, reading: Derksen Lecture 1.1, Krause 1.1-4) - Jan. 15: Basic properties of quiver representations and
finite dimensional algebras

(lecture notes, reading: Derksen Lecture 1.2-2.1, Krause Sec. 1.6,2.1-2) - Jan. 20: Krull-Remak-Schidt and path algebras

(lecture notes, reading: Derksen Lecture 3, Crawley-Boevey Sec. 1) - Jan. 22: Projective modules, projective resolutions

(lecture notes, reading: Derksen: Lecture 3, Krause: Sec. 1.5,1.7,

Crawley-Boevey: Sec. 1) - Jan. 27: Extensions between quiver representations

(lecture notes, reading: Derksen: Lecture 4) - Jan. 29: The structure of positive definite quivers

(lecture notes, reading: Derksen: Lecture 5.1-2, Krause: Sec. 4.1-4.3,

Crawley-Boevey: Sec. 2-5) - Feb. 3: Positive definite quivers and Dynkin diagrams

(lecture notes, reading: Derksen: Lecture 5.1-2, Krause: Sec. 4.1-4.3,

Crawley-Boevey: Sec. 2-5) - Feb. 5: Weyl groups and Reflection functors

(lecture notes, reading: Derksen: Lecture 5.3, Krause: Sec. 3) - Feb. 10: Coxeter functors and a second proof of Gabriel's
theorem

(lecture notes, reading: Derksen: Lecture 5.3, Krause: Sec. 4,5.1,

Crawley-Boevey: Sec. 6) - Feb. 12: Coxeter functors and a second proof of Gabriel's
theorem

(lecture notes, reading: Derksen: Lecture 5.3, Krause: Sec. 4,5.1,

Crawley-Boevey: Sec. 6) - Feb. 17: The derived category and Coxeter functors

(lecture notes, reading: Crawley-Boevey: Sec. 6) - Feb. 19: The classification of modules for affine quivers

(lecture notes, reading: Crawley-Boevey: Sec. 7-9) - Feb. 24: The classification of modules for affine quivers

(lecture notes, reading: Crawley-Boevey: Sec. 7-9) - Feb. 26: Auslander-Reiten quivers

(lecture notes, reading: Crawley-Boevey II: Sec. 1, you can also look at chapter 7

of Ringel and Schroer, but that's written in greater generality) - Mar. 3: Auslander-Reiten quivers and the knitting algorithm

(lecture notes, reading: Crawley-Boevey II: Sec. 1, Schiffler: Section 3) - Mar. 17: Auslander-Reiten theory in types A and D

(lecture notes, reading: Schiffler: Section 3) - Mar. 19: Wild quivers and quivers with relations

(lecture notes) - Mar. 24-31: class cancelled
- Apr 2: Cluster algebras

(lecture notes, there's a very nice introductory article by Lauren Williams) - Apr 7: Cluster categories

(lecture notes, there are lecture notes by Schiffler and a survey article of Reiten) - Apr 9: More on cluster categories

(lecture notes) - Apr 14: The Mackay correspondence

(lecture notes; most material is from Dolgachev's book and notes of Leuschke) - Apr 16: Hall algebras and Ringel's homomorphism (unquantized)

(lecture notes) - Apr 21: Hall algebras and Ringel's homomorphism (quantized)
- Apr 23: Canonical bases and quivers
- Apr 28: class presentations

This is not meant to be a comprehensive list, just possibilities you might consider.

- Cluster-tilted algebras ("Cluster-tilting theory" by Buan and Marsh) or other aspects of tilting theory
- Nakajima quiver varieties ("Lectures on Nakajima's Quiver Varieties" by Ginzburg)
- Quiver Grassmannians (for example, covering the theorem of Reineke that any projective variety can be realized as such)
- Bound quivers and finite dimensional algebras (There's lots of material in Ringel and Schroer)
- Derived categories (there is tons of material on this. Interesting sources include Thomas and Caldararu).
- Generic representation theory (Derksen, Lecture 12)
- Connection to Schur functors, Littlewood-Richardson coefficients (there's a lot on this in the later Derksen lectures. I think Lecture 8 is a good starting point).
- Properties of Coxeter elements in Weyl groups (Casselman has good pictures but is a little rough; there's also a short section in Heckman's book. The Wikipedia page is also pretty good.)
- Kac's theorem: for any quiver the dimension vectors of the indecomposables are the positive roots of the graph. (there are useful notes by Hubery)
- Hall algebras for coherent sheaves on elliptic curves (advanced; requires some algebraic geometry background. Maybe the best start is the notes of Schiffmann but there's also the original paper of Burban and Schiffmann)
- Perverse sheaves and the function-sheaf correspondence (advanced; probably requires some sheaf theory background. "What is a Perverse Sheaf" by de Cataldo and Migliorini is a good starting point.)
- Quivers with potential (part I and part II by Derksen, Weyman and Zelevinsky)
- Happel's characterization of hereditary categories with a tilting object ("A characterization of hereditary categories with tilting object" by Happel)