##### Department of Mathematics,

University of California San Diego

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### Colloquium

## Botong Wang

#### University of Wisconsin, Madison

## Enumeration of points, lines, planes, etc.

##### Abstract:

It is a theorem of de Bruijn and Erdos 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 â€œtop-heavyâ€ conjecture of Dowling and Wilson in 1975. I will give a sketch of the key idea of the proof, which uses the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. This is joint work with June Huh.

Host: James McKernan

### January 11, 2017

### 3:00 PM

### AP&M 6402

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