Ryan Kinser Contact information: Department of Mathematics University of Michigan 1852 East Hall 530 Church St. Ann Arbor, MI 48109-1043 Office phone: 734-763-2429 Personal page

Me in Sonoma Valley, March 2008

My main tools are functors that generalize the rank of a linear map to the setting of an arbitrary diagram of vector spaces and linear maps (a quiver representation). These functors can be used to construct numerical invariants of a quiver representation which include, as the simplest cases, its dimension vector and the ranks of all maps appearing in the representation.

Papers and notes

• The Rank of a Quiver Representation. J. Algebra (to appear). Preprint available at arXiv:0711.1135.
• Notes from my talk on the above paper at the University of Michigan Algebra seminar, 2007-11-20.
• Representation Rings of Rooted Tree Quivers (in preparation)
• Notes for a talk previewing the results of the above paper, at the International Conference on Representations of Algebras and Related Topics, Woods Hole, MA, 2008-04-26
• Notes for a talk on Gabriel's theorem in the UM Student Representation Theory seminar, 2008-02-20.

• ICRA XIII, August 2008, São Paulo, Brazil
• Summer School on Algebraic Geometry and Quiver Representations, Grenoble, France June 2008
• Maurice Auslander Lectures and International Conference on Representations of Algebras and Related Topics, Woods Hole, Massachussets, April 2008
• Combinatorial Representation Theory, March 2008, MSRI
• ICRA XII, July 2007, Toruń, Poland.