Online Talk: Tom Zaslavsky

YouTube recording:

Thursday, Feb 2, 3pm EST (8pm GMT, 9am Fri NZDT)

Speaker: Tom Zaslavsky, Binghamton University
Title: Matroids of gain signed graphs
Abstract: For standard affinographic hyperplane arrangements (a.k.a. deformations ofthe Type A root system arrangement or “braid” arrangement), integral gaingraphs give a simpler method to compute the characteristic polynomial, afundamental invariant.  For more general affinographic arrangements(a.k.a. deformations of the Type B root system arrangement), one has tocombine gains with signs.  How to do this has been a puzzle.  The obviousmethod is to put signs on top of gains.  The right method is to put gainson top of signs.  Laura Anderson, Ting Su, and I found out how to do this,constructing the natural matroid and the corresponding semimatroid, whichlatter gives the characteristic polynomial of these more generalarrangements when the gain group is the additive group of integers.  Iwill explain some of this.  It does get complicated.

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