BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Galen Dorpalen-Barry (University of Minnesota) DTSTART:20201109T200000Z DTEND:20201109T210000Z DTSTAMP:20260423T005649Z UID:YUAAS/13 DESCRIPTION:Title: C ones of Hyperplane Arrangements through the Varchenko-Gel’fand Ring\ nby Galen Dorpalen-Barry (University of Minnesota) as part of York Univers ity Applied Algebra Seminar\n\n\nAbstract\nThe coefficients of the charact eristic polynomial of an arrangement in a real vector space have many inte rpretations. An interesting one is provided by the Varchenko-Gel’fand ri ng\, which is the ring of functions from the chambers of the arrangement t o the integers with pointwise multiplication. Varchenko and Gel’fand gav e a simple presentation for this ring\, along with a filtration whose asso ciated graded ring has its Hilbert function given by the coefficients of t he characteristic polynomial. We generalize these results to cones defined by intersections of halfspaces of some of the hyperplanes. Time permittin g\, we will discuss Varchenko–Gel’fand analogues of some well-known re sults in the Orlik–Solomon algebra regarding Koszulity and supersolvable arrangements.\n LOCATION:https://researchseminars.org/talk/YUAAS/13/ END:VEVENT END:VCALENDAR