Any graph comes with a Jacobian, which is a real torus and is closely related to the celebrated matrix-tree theorem as well as the theory of chip-firing games. There is also an Abel--Jacobi theory, providing maps from a graph to its Jacobian. This picture gives rise to some interesting polyhedral geometry, some of which is related to the theory of random spanning trees. I will give an overview of the subject and state some recent results.
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