Date: Monday, April 15, 2013
Location: 4096 East Hall (3:00 PM to 4:00 PM)
Title: Categorical Homotopy from Quivers
Abstract: One question puzzled me for long time is "why do we do homological algebras on a `line' -- a linear complex?". If we want to deal with "n-stuff" instead of "bi-stuff", usually linear complexes are not enough. In this talk, I try to convince you that there are many other possibilities. I first quiver interpret the classical simplicial theory - including the cosimplex category, Dold-Kan correspondence, and Hochschild homology - as a certain Q-homotopy theory of type A. For the cyclic and cubical theories, we can proceed analogously. The point is that linear quivers can be replaced by other families of quivers. I will explain how to use representation theory of quivers to construct meaningful new theories. You will see a lot of examples. No knowledge on quiver representation is needed, just some homological algebra. (Joint with the Algebra Seminar.)
Speaker: Jiarui Fei
Institution: UC Riverside
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