Abstract:
This talk describes some aspects of the author's thesis work, giving an account of some interactions between the theory of oriented matroids, topology, and algebraic geometry. We first recall the basic notions and key results of oriented matroid theory used in the main theorems, and consider some relevant topological and geometric models. The first main result presented here provides a toric arrangement model of single-element liftings of regular matroids, yielding enumerative consequences for quotients of zonotopal subdivisions by lattice translation. After briefly describing the construction of these arrangements, we turn to some algebraic-geometric implications of counts, culminating with a formula for the class of certain compactified moduli spaces in the Grothendieck ring of varieties.
Note: Please note the special location, Smith 205. This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974