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PhD Preliminary Examination of Matthew Williams

November 15, 2023 @ 9:00 am - 5:00 pm

Advisor: Dr. Renzo Cavalieri

Committee: Dr. Maria Gillespie, Dr. Chris Peterson, Dr. Dustin Tucker

Title: Intersection Theory on the Moduli Spaces of Pseudostable Curves

Abstract: Intersection theory is a branch of algebraic geometry which studies the intersections of different geometric objects. Stable curves are relatively “nice” curves, in that the only singularities they have are nodes, and their intersections have long been researched. Pseudostable curves differ from their stable counterparts in that cusp singularities are allowed, but elliptic tails are disallowed, and this leads to a different intersection theory. An immensely useful tool in the intersection theory for stable curves is Mumford’s formula, and we present a pseudostable version of this formula and its applications.


November 15, 2023
9:00 am - 5:00 pm

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