##### Department of Mathematics,

University of California San Diego

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### Postdoc Seminar

## Andrew Zucker

#### UCSD

## Perspectives on the Halpern-Lauchli theorem

##### Abstract:

The aim of this talk is to introduce the audience to the Halpern-Lauchli theorem, which is a Ramsey-theoretic statement about products of trees. We will discuss several applications of the theorem and outline a number of different proofs. While the original proof was combinatorial in nature, there are now a number of proofs that interact with ideas from set-theoretic forcing. One of these proofs is new, and is joint work with Chris Lambie-Hanson.

### April 7, 2022

### 3:15 PM

APM B402A

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