2:00 pm Tuesday, March 28, 2006
Algebra Seminar: Non-Archimedean Polytopes and Cellular Resolutions by Josephine Yu (Univerisity of California, Berkeley) in RLM 10.176
Tropical convex hulls of finite sets of points are analogues of usual convex hulls, in the geometry over the tropical semiring (, min,+). In this talk, we will look at two connections between these and cellular resolutions. Tropical polytopes are usual polyhedral complexes and have natural structures of cellular free resolutions, i.e., their combinatorial data give rise to minimal free resolutions for some monomial ideals. On the other hand, they are also images of usual polytopes in an affine space over the Puiseux series field, under a non-archimedean valuation into the real numbers. For any monomial ideal, there is a family of polytopes over the Puiseux series field that give cellular resolutions of that monomial ideal. This family includes the hull complexes. Submitted by
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