# Sanjeevi Krishnan : Directed Poincare Duality

The max-flow min-cut theorem, traditionally applied to problems of maximizing the flow of commodities along a network (e.g. oils in pipelines) and minimizing the costs of disrupting networks (e.g. damn construction), has found recent applications in information processing. In this talk, I will recast and generalize max-flow min-cut as a form of twisted Poincare Duality for spacetimes and more singular "directed spaces." Flows correspond to the top-dimensional homology, taking local coefficients and values in a sheaves of semigroups, on directed spaces. Cuts correspond to certain distinguished sections of a dualizing sheaf. Thus max-flow min-cut dualities extend to higher dimensional analogues of flows, higher dimensional analogues of directed graphs (e.g. dynamical systems), and constraints more complicated than upper bounds. I will describe the formal result, including a construction of directed sheaf homology, and some real-world applications.

**Category**: Geometry and Topology**Duration**: 01:34:44**Date**: April 3, 2012 at 4:25 PM**Views**: 134-
**Tags:**seminar, Geometry/topology Seminar

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