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Galen Dorpalen-Barry: Varchenko-Gel’fand Ring of a "Cone" of a Hyperplane Arrangement

Time: Wed 2021-11-24 10.15 - 11.15

Location: Zoom meeting ID: 654 5562 3260

Participating: Galen Dorpalen-Barry (Ruhr-Universität Bochum)

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Abstract: The coefficients of the characteristic polynomial of an arrangement in a real vector space have many interpretations. An interesting one is provided by the Varchenko-Gel’fand ring, which is the ring of functions from the chambers of the arrangement to the integers with pointwise multiplication. Varchenko and Gel’fand gave a simple presentation for this ring, along with a filtration whose associated graded ring has its Hilbert function given by the coefficients of the characteristic polynomial. In this talk, I will generalize Gel'fand and Varchenko's results to "cones" defined by intersections of halfspaces of some of the hyperplanes.

Zoom meeting ID: 654 5562 3260

Zoom link:

The seminar can also be viewed in room 3721.