CACAAG Seminar
Wednesday, 8 Nov. 5:30 pm
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Venue: Ramanujan Hall.
Host: Madhusudan Manjunath.
Speaker: Trygve Johnsen.
Affiliation: The Arctic University of Norway.
Title: Geometry of matroids, with a view toward application in coding theory.
Abstract: We will try to explain some of the material in "Matroid Theory for Algebraic Geometers" by Erik Katz, and "Simplicial Generation of Chow rings of Matroids" by Bachman, Eur & Simpson. Here one associates geometric objects like toric varieties with matroids and describes the fans that give rise to them. One also describes Chow rings of matroids, and how the (Bergman fan of a ) matroid itself can be viewed as an element of the Chow ring, or Minkowski weight, for a (usually) "larger " uniform matroid. If time permits, we will mention briefly how Chow rings can be defined also for q-matroids, an object arising from rank metric codes, analogous to how usual matroids are a tool to describe codes with the Hamming distance.