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Abstract:
The Riemann-Roch theorem is fundamental to algebraic geometry.
In 2006, Baker and Norine discovered an analogue of the Riemann-Roch
theorem for graphs. In fact, this theorem is not a mere analogue but has
concrete relations with its algebro-geometric counterpart. Since its
conception this topic has been explored in different directions, two
significant directions are i. Connections to topics in discrete geometry
and commutative algebra ii. As a tool to studying linear series on
algebraic curves. We will provide a glimpse of these developments. This
talk is based on joint work with i. Omid Amini, ii. Bernd Sturmfels, iii.
Frank-Olaf Schreyer and John Wilmes.
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