### Schedule:

2:00-3:00 Martino Lupini (Caltech)

3:15-4:15

Geoff Galgon (UCI)
4:15-5:00 Coffee Break

5:00-6:00 Spencer Unger (UCLA)

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### Abstracts:

**Martino Lupini**
**Title:** Weak equivalence of actions and first order logic

**Abstract:** I will present a model-theoretic perspective on
the notion of weak equivalence for actions on the standard
probability space. I will explain how this perspective allows one
to recover some know results about the space of weak equivalence
classes, and at the same time establish their noncommutative
analogs.This is joint work with Peter Burton.

**Geoff Galgon**
**Title:** Perfect and Scattered Subsets of 2^{\kappa} and
P_{\kappa}\lambda,

with an Application to Almost Disjoint Refinements

**Abstract:** The topological notions of perfectness and
scatteredness can be

generalized in several ways to spaces like \kappa^{\kappa},
2^{\kappa},

and P_{\kappa}\lambda. We present one possible way of doing this,
and show

as an application how the consistency of a Cantor-Bendixson-like
dichotomy

for closed subsets of \kappa^{\kappa} can be used to prove that in
generic

extensions by a broad class of forcings, there is an almost
disjoint

refinement of the ground model's \kappa-sized subsets of \kappa.

**Spencer Unger**
**Title:** Successive failures of weak square and the failure
of SCH

**Abstract:** We are motivated by the question "Can one
construct a kappa-Aronszajn tree for some kappa > aleph_1 in
ZFC?" Towards a negative answer, we prove the following
theorem: From large cardinals it is consistent that
aleph_{omega^2} is strong limit and there are no special
kappa-Aronszajn trees for any regular kappa in the interval
[aleph_2, aleph_{omega^2+2}].

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### Organizers:

Alexander Kechris (Caltech).

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Itay Neeman (UCLA).

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Matthew Foreman (UCI).

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Martin Zeman (UCI)

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#### Local Organizers:

Alexander Kechris (Caltech)

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Martino Lupini (Caltech)

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