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Name: Dr. Calin Chindris
Address: Department of Mathematics, University of Iowa,
Iowa City, IA 52246, U.S.A.
Office: 1N MLH
Phone: (319) 335-0764
Email: calin-chindris@uiowa.edu (or cchindri@math.uiowa.edu)
Webpage: http://www.math.uiowa.edu/~cchindri
Office hours: MW 10:30-11:30AM, F 11:00-12:00PM
Course description: A quiver is just a directed graph
and a quiver representation assigns a vector space to each vertex
and a linear map to each arrow. Quivers and their representations occur
naturally in the representation theory of algebras but they also have
interesting connections with other areas such as the representation theory
of general linear groups (tensor product multiplicities), root systems
for Lie algebras, cluster algebras, algebraic geometry (quotient varieties) and
physics (string theory). The first part of the course covers classical aspects
of the theory including Gabriel's famous classification of quivers of finite
representation type and root systems for quivers. The second part of the
course is an introduction to quiver invariant theory. The main objects of
study are the algebras of semi-invariants and stability conditions of quivers.
The goal is to provide a general framework for understanding and
solving a series of important problems revolving around tensor product
multiplicities for GLn (Knutson-Tao saturation theorem, Okounkov's
log-concavity (ex)-conjecture) and cluster algebras (categorification,
cluster fans).
Prerequisites: Standard courses in algebra at the level of 22M:205 and 22M:206. (I will try to make the course essentially self-contained.)
Grading: Based on attendence and ocassional homework problems.
Syllabus: Lecture 22M:330:002
Required Textbook: None. The following online lecture notes will also be useful for the course:
Standard reference books for representations of finite dimensional algebras are:
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Ibrahim Assem, Daniel Simson, Andrzej Skowronski, Elements of the representation theory of associative algebras. Vol. 1,2,3. London Mathematical Society Student Texts, 65. Cambridge University Press, Cambridge.
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Maurice Auslander, Idun Reiten, Sverre Smalo, Representation theory of Artin algebras. Cambridge Studies in Advanced Mathematics, 36. Cambridge University Press, Cambridge, 1995. xiv+423 pp.
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