Abstract: Homological Algebra is essentially the study of derived functors such as Ext and Tor. Today the derived functors are studied using the idea of derived category. We will explore these concepts as well as Quillen's approach to handling the derived category (and hence derived functors). We will then present a new Quillen structure on the derived category associated to both R-Mod (modules over a commutative ring with 1) and O-Mod (sheaves over a ringed space O). In the latter case, this is the first "monoidal model structure" one has found on the category of complexes of O-modules. One benefit is that this puts the derived functor Tor into a logical framework and also gives an alternate definition of Ext.

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If you are interested in giving a talk, please contact Dr. Juan Gil, the Colloquium Coordinator for the Fall 2005 semester.