Feb

16

Fri

Continuing the theme of symbolic dynamics, I will demonstrate a proof of Simpson’s result that “Entropy = Dimension” for N^d and Z^d, and discuss some of Adam Day’s work generalizing these results to amenable groups.

Feb

23

Fri

This week Umar Gaffar will give Shelah’s proof of the following result:

Let $\lambda$ be the cardinality of an ultraproduct of finite sets. If $\lambda$ is infinite then $\lambda=\lambda^{\aleph_0}$.

Mar

23

Fri

David Webb will continue to discuss results from Adam Day’s paper on amenability and symbolic dynamics.

Apr

6

Fri

This week in the Logic Seminar in Keller 314, David Ross will give an easy proof of a slight extension of a result of Lagarias on the Diophantine equation

$$ c(1/x_1+cdots+1/x_s)+b/(x_1 x_2cdots x_s)=a$$

The proof will be nonstandard, but really only require a sufficiently-saturated ordered field extension of $mathbb R$.

Apr

13

Fri

Mushfeq Khan will coninue to speak on amenability and symbolic dynamics. The focus will be the Ornstein-Weiss combinatorial

lemmas from Adam Day’s paper.

## University of Hawaiʻi at Mānoa 2018