seminar: Divisors on graphs, orientations and system reliability
speaker: Fatemeh Mohammadiabstract: Associated to every coherent system there is a canonical ideal whose Hilbert series encodes the reliability of the system. We study various ideals arising in the theory of system reliability. Our main contribution is to apply the syzygy tool from computational algebra to distinguish the (non-cancelling) terms in the reliability formula for various systems. This gives a more clear insight into the structure of each such system. Using ideas from the theory of divisors, orientations, and matroids on graphs we describe the minimal polyhedral cellular resolution of these ideals. In each case, we give an explicit combinatorial description of the minimal generation set for each higher syzygy module. This resolves open questions posed by Giglio-Wynn and develops new connections between the theory of oriented matroid, the theory of divisors on graphs, and the theory of system reliability.
timetable:
Mon 23 Feb, 9:30 - 10:30, Aula Dini
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