[Settfa] Fwd: Wednesday seminar

[Wieslaw Kubis]

Dear All,

I'm forwarding the announcement concerning two seminar talks this week 
(both in the Blue Lecture Room).

All the best,

Wieslaw



================================



There will be two seminar talks by Justin Moore next week, both in the 
blue lecture hall (NOTE THE LOCATION CHANGE!).
On Tuesday July 1st the seminar meets at 10:00 in the Institute of 
Mathematics CAS, Zitna 25, blue lecture hall, ground floor, rear building.
On Wednesday July 2nd the seminar meets at 11:00 in the Institute of 
Mathematics CAS, Zitna 25, blue lecture hall, ground floor, rear building.


Program Tuesday: Justin Moore -- Some set-theoretic strategies for 
proving Thompson's group is amenable.

This informal talk outlines two strategies for proving that Thompson's 
group is amenable. This will bring together an unlikely combination of 
topics: ultrafilter dynamics of algebraic structures, Galton-Watson 
processes, rank-to-rank elementary embeddings, and Laver tables.



Program Wednesday: Justin Moore -- Uniform ultrafilters on omega_1 and 
their complexity

This talk will investigate uniform ultrafilters on $\omega_1$, both with 
respect to the Tukey order and the Rudin-Kiesler order. We show that it 
is independent of ZFC (modulo a large cardinal assumption) that every 
uniform ultrafilters on $\omega_1$ has the maximum Tukey-type. We also 
show that PFA implies that Todorcevic's ultrafilter $\mathcal{U}(T)$ has 
the maximum Tukey type of a directed set of cardinality $2^{\aleph_1}$.
We also show that PFA implies that $\mathcal{U}(T)$ is minimal in the 
Ruden-Kiesler order with respect to being a uniform ultrafilter on 
$\omega_1$ and that it admits a finest partition. This is joint work 
with Tom Benhamou and Luke Serafin.


Best,
David