Colloquium: "Enumeration of Points, Lines, Planes, Etc."
Botong Wang, University of Wisconsin-Madison
Abstract: It is a theorem of de Bruijn and Erdős that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. If time allows, I will also talk about a log-concave conjecture of Welsh and Mason. The new results in this talk are joint work with June Huh.
Tea @ 3:45 in Cupples I, Room 200
Host: John Shareshian