INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
Thematic Program on Forcing and its Applications
Andreas Blass (U. Michigan), Alan Dow (U. North Carolina,
Justin Tatch Moore (Cornell), Juris Steprans (York U.),
Stevo Todorcevic (U. Toronto)
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)
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updates on the program please subscribe to our mailing list at www.fields.utoronto.ca/maillist
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
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
(starting the week of Sept. 17)
Course on Forcing
Alan Dow (UNC Charlotte)
Tuesdays and Thursdays 11:00 a.m. - 12:30 p.m.
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.
-Updated notes for the course for Sept 25 and Sept 27
on discussion about the Kunen and Miller results for the Cohen
Notes from October 2
Course on Large Cardinals
Paul Larson (Miami University)
Tentatively Tuesdays and Thursdays 1:30 p.m. - 3:00 p.m.
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
Taking the Institute's Courses for Credit
As graduate students at any of the Institute's University Partners,
you may discuss the possibility of obtaining a credit for one or
more courses in this series with your home university graduate officer
and the course instructor. Assigned reading and related projects
may be arranged for the benefit of students requiring these courses
September 8-9, 2012
Appalachian Set Theory Workshop
C*-algebras, classification and descriptive set theory
September 10-14, 2012
Workshop on Applications to Operator
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 22-26, 2012
Workshop on Forcing Axioms and their
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
Organizers: Michal Hrusak, Paul Larson, Saharon Shelah, W. Hugh
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
November 7-9, 2012,
Distinguished Lecture Series
Matthew D. Foreman, University of California, Irvine
Postdoctoral Fellows and Program Visitors
The Thematic Program on Forcing and its Applications
is pleased to welcome the following Postdoctoral
Fellows to the Program.
|Fields Postdoctoral Fellows
David Chodounsky, PhD (Charles University in Prague, 2011)
Miguel Angel Mota, PhD (University of Barcelona, 2009)
Tristan Bice, PhD (Kobe University, 2012)
|Trevor Wilson, PhD (University
of California, Berkeley, 2012)
Sean Cox, PhD (University of California, Irvine, 2009)
Brent Cody, PhD (City University of New York Graduate Center, 2011)
All scientific events are open to the mathematical sciences community.
Visitors who areinterested in office space or funding are
requested to apply by filling out the application form (now closed).
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.
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