3:45PM: From stable curves to higher dimensions
Location: 740 EvansApplications of stable curves and maps to enumerative geometry, physics, arithmetical geometry, symplectic geometry, etc., are very well known. Due to efforts by many people, this theory was partially extended to higher dimensions, when stable curves are replaced by stable surfaces, 3-folds, etc. I will attempt to describe the current state of the art in this field.
5:00PM: Linear series on curves and graphs
Location: 740 EvansI will discuss some unexpectedly rich analogies between algebraic curves and finite graphs, including graph theoretic-analogues of the Jacobian, the Riemann-Roch theorem, and hyperellipticity. I will then discuss how specialization of linear series from the generic fiber of a regular semistable arithmetic surface to the dual graph of the special fiber provides a concrete link between these two worlds.