Category Archives: Thematic Program on Forcing and its Applications

Forcing and its applications: Retrospective Workshop, March 29 – April 2, 2015

The meeting will take place at the Field Institute, 222 College Street, Toronto.

About

In the years 1963-1964, Paul Cohen developed the method of forcing in order to settle Cantor’s Continuum Problem.  Since then, the method of forcing has been adapted into a broadly applicable technique for showing that a given statement is
consistent with the axioms of mathematics.

OVERVIEW 

The fall 2012 thematic program at the Fields Institute on Forcing and its Applications witnessed breakthroughs in both the internal study of set theory as well as its applications to fields such as analysis and the general theory of topological groups. This workshop will bring together experts studying different aspects of set theory related to the program — large cardinals, singular cardinals, infinite combinatorics, and forcing axioms — as well as closely related fields of mathematics such as functional analysis and topology.

 

Schedule:

***

Day 1: Sunday March 29, 2015.
Time Speaker Title
9:30-10:30am Alan Dow (University of North Carolina)
10:30-11:00am
Coffee
11:00-12:00pm Juris Steprans (York University)
12:00-2:00pm
Lunch
2:00-3:00pm Jindrich Zapletal (University of Florida)
3:00-3:30pm
Coffee
3:30-4:30pm Sean Cox (Virginia Commonwealth University)

***

Day 2: Monday March 30, 2015.
Time Speaker Title
9:30-10:30am Spencer Unger (UCLA)
10:30-11:00am
Coffee
11:00-12:00pm Christina Brech (University of São Paulo)
12:00-2:00pm
Lunch
2:00-3:00pm John Krueger (University of Northern Texas)
3:00-3:30pm
Coffee
3:30-4:30pm Dima Sinapova (University of Illinois, Chicago)

***

Day 3: Tuesday March 31, 2015.
Time Speaker Title
9:30-10:30am Michael Hrusak (UNAM, Morelia)
10:30-11:00am
Coffee
11:00-12:00pm Jordi Lopez-Abad (Instituto de Ciencias Matematicas)
12:00-2:00pm
Lunch
2:00-3:00pm Maryanthe Malliaris (University of Chicago)
3:00-3:30pm
Coffee
3:30-4:30pm Heike Mildenberger (Albert Ludwigs Universität Freiburg)

***

Day 4: Wednesday April 1, 2015.
Time Speaker Title
9:30-10:30am Dana Bartošová (University of Toronto)
10:30-11:00am
Coffee
11:00-12:00pm Yinhe Peng (Chinese Academy of Science)
12:00-2:00pm
Lunch
2:00-3:00pm Natasha Dobrinen (University of Denver)
3:00-3:30pm
Coffee
3:30-4:30pm Assaf Rinot (Bar-Ilan University)

***

Day 5: Thursday April 2, 2015.
Time Speaker Title
9:30-10:30am Matteo Viale (University of Torino)
10:30-11:00am
Coffee
11:00-12:00pm Miguel Mota (University of Toronto)
12:00-2:00pm
Lunch
2:00-3:00pm Konstantinos Tyros (University of Warwick)
3:00-3:30pm
Coffee
3:30-4:30pm Marcin Sabok (McGill University)

Organizing Committee

  • Justin Moore (Cornell University)
  • Stevo Todorcevic (University of Toronto)

Workshop on Iterated Forcing and Large Cardinals, November 12-16, 2012

This workshop will take place at the Fields institute, as a part of the 2012 Thematic Program on Forcing and its Applications.

Organizing Committee:

  • Michal Hrusak
  • Saharon Shelah
  • W. Hugh Woodin

Distinguished Lecture Series: Matthew D. Foreman, November 7-9, 2012

Distinguished Lecture Series
November 7-9, 2012 at 3:30 p.m.
Fields Institute, Room 230

Matthew D. Foreman
University of California, Irvine
November 7, 2012 at 3:30 pm.
Large Cardinals: Who are they? What are they doing here? Why won’t they go away?

This lecture will discuss the roots of large cardinals, (starting from Euclid), trace their evolution and survey some present day results.
Aimed at a general audience, the talk will avoid technical language as much as possible. While no one may change their mind about
large cardinals, everyone will leave having a better insight into what they are.

November 8, 2012 at 3:30 pm.
Does set theory have anything to do with mathematics?

We discuss the relationship of Set Theory with other branches of mathematics and the role it has historically played. We will give some recent examples and discuss one–the classification problem for ergodic measure preserving transformations–in some depth.

November 9, 2012 at 3:30 pm.
Generic Elementary Embeddings

Conventional large cardinals have been codified to have a certain form–postulating class sized objects. Though these are well-understood to have “equivalent” statements in ZFC, they don’t actually “live in V”. One can stipulate some very similar objects that can be thought of as “generic” large cardinals. The equivalent ZFC versions of these objects can have small cardinalities. As a result they are directly relevant to questions such as the Continuum Hypothesis. Moreover, generic elementary embeddings have become an essential technique for extracting consequences of large cardinals involving sets of small cardinality.
This lecture will show that a broad class of generic elementary embeddings is equiconsistent with their analogous large cardinals. The results include equiconsistency results between combinatorial properties of the first few uncountable cardinals and huge cardinals.

Workshop on Forcing Axioms and their Applications, October 22-26, 2012

This workshop will take place at the Fields institute, as a part of the 2012 Thematic Program on Forcing and its Applications.

Organizing Committee:

  • Jordi Lopez Abad
  • Justin Tatch Moore
  • Stevo Todorcevic

 

 

Graduate course on Large Cardinals

starting the week of Sept. 17

Course on Large Cardinals
Paul Larson (Miami University)

Tuesdays and Thursdays 1:30 p.m. – 3:00 p.m.
Stewart Library, Fields Institute
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.

 

Graduate course on Forcing

starting the week of Sept. 17

Course on Forcing
by Alan Dow
(UNC Charolette)

Tuesdays and Thursdays 11:00 a.m. – 12:30 p.m.
Stewart Library, Fields Institute

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.

Workshop on Applications to Operator Algebras, September 10-14, 2012

This workshop will take place at the Fields institute, as a part of the 2012 Thematic Program on Forcing and its Applications.

Organizing Committee:

  • Ilijas Farah
  • Andrew Toms
  • Alexander S. Kechris

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Stevo Todorcevic: Walks on Ordinals and Their Characteristics

Centre de recherches mathematiques
Fields Institute
Pacific Institute for the Mathematical Sciences


September 6, 2012
at 3:30 p.m.
2012 CRM-Fields-PIMS Prize Lecture

Stevo Todorcevic, University of Toronto
at Fields Institute

 

Title: Walks on Ordinals and Their Characteristics

Abstract: Discovering new canonical structures in set theory such as, for example, the Hausdorff gap or the Aronszajn tree are rare phenomena. This is particularly true when the structures are not countable due to the fact that the set-theoretic independence results are much more frequent in that realm. Characteristics associated to walks on ordinals have shown to be a powerful technology in discovering and describing canonical structures of set theory. This lecture will present some of the best known such characteristics together with the canonical structures they lead to.