Faculty Research Perspectives

Triangulated Categories

Chuck Weibel

April 7, 3:30 PM in Hill 705



Abstract.

What are triangulated categories, and what are they good for? The derived category (say of modules over a ring) used to be the standard example of a triangulated category, and it is used to refine invariants. We can ask: when is a triangulated category the derived category of something? When is it the derived category of several things? What information do we need in order to decide these things? In higher Mirror Symmetry, for example, this issue plays a central role. There are now enhancements, coming from algebra and topology, which maybe offer clues about these questions.

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