Young Set Theory Workshop 2009

The goal of these conferences is to bring together PhD students and
postdocs in set theory in order to learn from senior researchers in
the field, hear about the latest research and to discuss research
issues in small focused groups.

The second Young Set Theory Workshop will take place between 14-18
April 2009 at the CRM (Mathematics Research Center) in Bellaterra,
near Barcelona (http://www.crm.es).

The conference format will be as follows:
Four senior set theorists have been invited to represent a branch of
Set Theory and give morning tutorials about their work.

The afternoons will be devoted to small group discussion sessions
which will be organised as follows. All participants will be asked to
write a one-page statement about their research. These statements
will be organised into branches of set theory and presented at the
conference. Based on the research statements, specific discussion
sessions will be formed for those working in similar areas and more
general sessions for those interested in getting an overview of the
latest research in each branch of set theory.  At the end of the day,
we will meet altogether again to hear a talk by an outstanding invited
postdoc.

All accommodation and meals will be at the Vila Universitaria of the
UAB (which is about 30 minutes from Barcelona by train) on the same
campus as the CRM. Accommodation at Vila Universitaria will be
available from a 13-18 April 2009. Due to space limitations, rooms
will have to be shared and registration may be limited.  More and
updated information, in particular details of registration,
accommodation, travel grants and conference fee will be available at
the following website:
http://wwwmath.uni-muenster.de/logik/YS09/

Organisers:
David Aspero (david.aspero@icrea.es)
Neus Castells (n.castells@ub.edu)
Gunter Fuchs (gfuchs@math.uni-muenster.de)
Bernhard Irrgang (irrgang@math.uni-bonn.de)
Miguel Angel Mota (motagaytan@gmail.com)
Katie Thompson (aleph_nought@yahoo.com)
Jip Veldman (veldman@math.uni-bonn.de)
Matteo Viale (matvial@logique.jussieu.fr)

2nd European Set Theory Meeting

Organizers: G. Plebanek, R. Schindler, J. Vaananen, B. Velickovic

The goal of European Set Theory Meetings is to bring together most active researchers in this subject from Europe with the goal of creating a European network in set theory. While the meeting will be European in character it will be open and we plan to invite a number of leading experts in the field from the US and other parts of the world. Particular emphasis will be given to supporting young European graduate students and postdocs. Poland was selected as the host of this meeting since researchers from Poland have played a special role in its development from the early days of the subject. In particular, we hope that a number of Polish and other European mathematicians working outside of Europe will be able to attend and thus strengthen their ties with the scientists working in Europe. This current meeting will be the second in this series. The first meeting took place in Bedlewo July 9 to 13, 2007 and has attracted over 80 mathematicians, among them some of the leaders in this subject.

The scientific topics of the meeting will cover the three principal areas of set theory.

The first topic is foundations of mathematics. While the usual axioms ZFC of set theory are sufficient for most of mathematics, it is well that they are incomplete and in particular do not decide some of the basic questions of set theory such as the Continuum Hypothesis as well as its generalizations and variations. Set theorists have been searching for natural extensions of these axioms which would decide these open problems. There are two basic types of additional axioms which are considered: large cardinal axioms, which postulate that the set theoretic universe is “tall”, and forcing axioms which postulate a certain form of saturation of the set theoretic universe. Both of these directions reinforce Gödel’s basic intuition that additional axioms of set theory should be certain forms of maximality principles.

The second direction is descriptive set theory which studies properties of definable sets of reals, and more generally Polish spaces. In recent years a number of important developments have brought descriptive set theory closer to ergodic theory, dynamical systems and the theory of group representations. This connections is achieved through the study of orbit equivalence relations and the corresponding quotient spaces. While these spaces are singular, i.e. the Borel structure on them is degenerate, it is possible to study their properties by lifting them to the original space.

Finally, combinatorial set theory deals with uncountable structures without any definability restrictions. Most of the questions in this area are independent of ZFC and their study requires the use of Cohen’s method of forcing. In recent years, remarkable results have been obtained in this area and some of the most outstanding open problems have been solved.

We intend to have two mini courses by prominent researchers, one from “pure” set theory and one at the interface of set theory and some other area of mathematics such as Banach space theory. In addition, we will have around 20-25 lectures of 30-50 min each. The total number of participants is expected to be around 60-80. The meeting will take place July 6-10, 2009 at the Mathematical Research and Conference Center, Będlewo Poland.

For the program and all further information please visit  www.esf.org/conferences/09306 . Note that the closing date for applications is April  8 2009.

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