Title: 8 implies 9 and beyond
Abstract: Several classical incidence theorems of projective geometry, such as Pascal's Theorem and Pappus' Theorem, are special cases of Cayley-Bacharach, which states that if nine points in the plane are the intersection of two cubic curves, then a cubic curve passing through any eight of those nine points must necessarily pass through the ninth.
In this talk we'll discuss interpolation problems, prove Cayley-Bacharach, and see how it implies the theorems of Pappus and Pascal. Time permitting, we'll also see how we can upgrade Cayley-Bacharach to a statement about certain moduli spaces of surfaces.
Note: The talk will start at 4:10 pm
Daniel Mallory
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