Saturday, February 23, 2013

Rowland Hall 306

Funded by NSF Grant DMS-1044150


2:00 - 3:00  Trevor Wilson (UCI)

3:30 - 4:30  Robin Tucker-Drob (Caltech)

5:00 - 6:00  Ryan Holben (UCI)

Abstracts    Driving directions and parking    Organizers   Previous meetings  

Abstracts of the talks:  

Trevor Wilson:   Scales on Pi^2_1 sets

Abstract: Scales are used in descriptive set theory as a way to uniformize sets in the plane, often in the context of the Axiom of Determinacy (AD) or its natural strengthening AD^+.  Although AD contradicts the Axiom of Choice, uniformization principles can be considered as weak forms of choice and so their co-existence with AD is a rather subtle issue.  A well-known theorem of Woodin gives scales on Sigma^2_1 sets.  The natural next step is the construction of scales on Pi^2_1 sets, which requires some additional hypothesis beyond AD^+.  We discuss existing results and then present a method to produce a scale of optimal complexity---namely, the norms of the scale are definable from ordinals.

Robin Tucker-Drob:  Shift-minimal groups and cost    

Abstract: A countable group G is called shift-minimal if all non-trivial measure preserving actions weakly contained in the Bernoulli shift of G are free. I will discuss the connection between shift-minimality, cost, and certain properties of the reduced C*-algebra of G, indicating the proof that if a countable group G admits a free measure preserving action of cost strictly greater than 1 then there is a finite normal subgroup N of G such that G/N is shift-minimal. This implies shift-minimality for a wide variety of groups including all non-abelian free groups. I will also discuss a number of open questions related to shift-minimality and cost.

Ryan Holben:  Square at Singular Cardinals

Abstract: Square principles refer to a family of infinitary combinatorial principles which are studied in set theory. Square is intimately related to a number of other principles such as the tree property and stationary set reflection. Finding the consistency strength of these principles at small singular cardinals is an interesting and difficult problem which relates to the Singular Cardinal Hypothesis. We look at some classical theorems which tie these results together, then introduce some of our own results and discuss the methods needed.

Driving directions and parking: 

For maps, and other travel information click here. Rowland Hall is building 400 on the map.

From the north:

From the south:

To park on campus you will need to purchase a parking permit. You can buy a parking permit from the dispenser near the entrance to lot 16. Park in lot 16. Parking may cost as much as $14 for the full day. That kiosk takes both cash and credit cards. Quarterly or annual parking permits from other UC campuses are honored at UCI (more information on parking permit reciprocity is available here).

Organizers:  Alexander Kechris, Itay Neeman, Martin Zeman 

Local organizer: Martin Zeman 

Previous meetings: 

Caltech, November 17, 2012

UCLA, May 12, 2012

Caltech, February 18, 2012

UCI December 3, 2011