July-December 2012
Thematic Program on Forcing and its Applications

Organizers
Andreas Blass (U. Michigan), Alan Dow (U. North Carolina, Charlotte),
Justin Tatch Moore (Cornell), Juris Steprans (York U.) Stevo Todorcevic (U. Toronto)

Scientific advisory committee
Andreas Blass (Michigan, Ann Arbor), Sy-David Friedman (Kurt Gödel Research Center),
Alexander S. Kechris (California Institute of Technology), Menachem Magidor (Hebrew Univ.),
Saharon Shelah (Hebrew Univ. & Rutgers Univ.), Jouko Väänänen (Univ. of Amsterdam & Helsinki)
W. Hugh Woodin (UC, Berkeley)

Application for participation support	Program Postdoctoral Fellowships	Hotels and Housing
Registration (open in early 2012)	Confirmed Participants	Visitor Information

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Outline of Scientific Activities

The semester will starts with a week-long summer school. The activities during the summer school include mini-courses and lectures designed to prepare the students and other participants for the semester.

Seminars

The program will also include a weekly seminar. This will be a continuation of the weekly Toronto Set Theory seminar, currently meeting at the Fields Institute

Graduate courses

Course on Forcing.
This will be a basic Forcing course directed towards graduate students and non-experts which will still reach a reasonable level of sophistication in designing forcing notions. An emphasis will be placed on examples and on the methodology of designing the forcings themselves rather than the formal and rigorous development of the logical underpinnings of forcing.

Course on Large Cardinals
Large cardinal axioms, also known as the axioms of the higher infinite, posit cardinals that prescribe their own transcendence over smaller cardinals and provide a superstructure for the analysis of strong propositions in set theory. They form an essentially linear hierarchy reaching up to inconsistent extensions of motivating concepts. This course will focus on the most fundamental large cardinal notions, emphasizing their inter-relationship with combinatorics and with forcing techniques.

Workshops

September 10-14, 2012
Workshop on Applications to Operator Algebras
Organizers: Ilijas Farah, Andrew Toms, Alexander S. Kechris
This workshop will explore connections between set theory and C*-algebras, as well as the emerging connections with von Neumann algebras. Some long-standing problems from the theory of C*-algebras were recently solved by using increasingly sophisticated set-theoretic tools. Emphasis will be put on applications of forcing to still unsolved problems, such as the general Stone-Weierstrass problem or the consistency of a positive answer to Naimark's problem. Part of the workshop will be devoted to the emerging connections between the classication problems in operator algebras and the abstract classication program in descriptive set theory.

October 15-19, 2012
Workshop on Forcing Axioms and their Applications.
Organizers: Jordi Lopez Abad, Justin Tatch Moore, Stevo Todorcevic
This workshop will bring together researchers working on combinatorial analysis of Banach spaces and those specializing in forcing axioms. Central to the discussion will be combinatorial consequences of Martin's Maximum which are driven by applications and which are readily accessible to those working in analysis and other fields. The driving goal will be to progress our understanding in well known open problems in the the theory of Banach space such as the metrization problem for compact convex sets, the smooth bump problem, and the separable quotient problem.

November 12-16, 2012
Workshop on Iterated Forcing and Large Cardinals
Organizers: Michal Hrusak, Saharon Shelah, W. Hugh Woodin
This workshop will focus on preservation theorems for iterated forcing constructions. The goal is to better understand when iterated forcing constructions preserve the Continuum Hypothesis and its strengthenings and also certain inequalities of cardinal invariants of the continuum. An additional focus will be to attempt to better understand the relationship between Woodin's Pmax-machinery and more conventional iterated forcing constructions. Work of Shelah and Woodin already hints that large cardinals will likely play a role in studying when reals are added in iterated forcing constructions.

Distinguished and Coxeter Lecturers

October/November 2012, Distinguished Lecture Series
Matthew D. Foreman, University of California, Irvine

Postdoctoral Fellows and Program Visitors

We will support a number of Fields postdocs for the duration of the program, as well as offer support towards a visitors' program, including visiting Ph.D. students

All scientific events are open to the mathematical sciences community. Visitors who are interested in office space or funding are requested to apply by filling out the application form. Additional support is available (pending NSF funding) to support junior US visitors to this program.
Fields scientific programs are devoted to research in the mathematical sciences, and enhanced graduate and post-doctoral training opportunities. Part of the mandate of the Institute is to broaden and enlarge the community, and to encourage the participation of women and members of visible minority groups in our scientific programs.

Postdoctoral fellowship applications for additional information see postdoctoral web page.

For additional information contact thematic@fields.utoronto.ca

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