|Date: Friday, January 17, 2014
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Building vector spaces from sets
Abstract: The representation theory of symmetric groups converts bijective functions to invertible matrices; in this talk, we drop the assumptions of bijectivity and invertibility. The resulting mathematics is called ``the representation theory of the category of finite sets.'' I will give natural examples of such representations arising in topology, geometry, and combinatorics, including applications to configuration spaces and the coordinate rings of combinatorial embeddings. The main theorem is a homological result about the projective resolutions in the category of all representations. Finally, I will show how the theory gives algorithms for the concrete task of manipulating vector space presentations. This work is inspired by the theory of ``representation stability'' due to Church-Farb and Church-Ellenberg-Farb.
Speaker: John Wiltshire-Gordon
Institution: U. Michigan