Abstract:
Given a directed, acyclic graph \$G\$ with capacity 1 on every edge and netflow vector \$a\$, the set of all flows of value 1 under \$a\$ in \$G\$ forms a polytope, \$\mathcal{F}_G(a)\$, which we call a flow polytope. When considering the unit flow vector \$a = (-1,0,\dots,0,1)\$, the vertices of \$\mathcal{F}_G(-1,0,\dots,0,1)\$ correspond with the routes from source to sink in \$G\$, allowing us to form a connection between graphs and convex geometry. In this talk, we note that a graph is simply a 1-dimensional simplicial complex and consider how we can generalize flow polytopes to this setting. For a pure \$d\$-dimensional simplicial complex \$X\$, we define an analogous \$\mathcal{F}_X(a)\$ and study properties of these so-called higher flow polytopes. This talk is based on joint work with Rupert Li.
Note: 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