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Mathematics Colloquium


Date:  Tuesday, March 22, 2016

Title:  Tensor triangular geometry of stable homotopy categories

Abstract:  Tensor triangular geometry provides a unified framework in which to study structural properties of triangulated categories with a compatible tensor (i.e. symmetric monoidal) product. Examples of such categories include: * perfect complexes over a commutative ring, * the derived category of G-modules for G a finite group, * the Spanier-Whithead stable homotopy category, * the stable G-equivariant homotopy category, and * the stable motivic homotopy category. I will survey the constructions and successes of tensor triangular geometry, and then describe a particularly important comparison map between the tt-spectrum of a tt-category C and the Zariski spectrum of the endomorphisms of the unit object in C. Recent work of Heller, Thornton, and myself uses this map to study the tensor triangular geometry of the stable motivic homotopy category.

Speaker:  Kyle Ormsby
Institution:  Reed College


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