Neostability theory (12w5045)

Objectives

The main objective is to understand what is known and what needs to be done in the foundational work of four related fields: dependent theories, the topology of generically stable types in dependent theories, the role of non forking outside stable theories and the applications to additive combinatorics, and the common ideas behind dp-miniality, dp-rank, burden and VC-density.

Such a meeting would need to have a good equilibrium between formal presentations of the current results and active discussion of open problems and the connections between the different concepts, and collaborations.

As mentioned in the overview, in the last decade this subject has attracted the interest of many researchers; this interest has sometimes happened independently and the different approaches, the concepts, and some of the results are not all spread out between the members of the community. This are some of the reasons we feel it is of utmost importance to have a meeting where the most active researchers in this subject come together and share and discuss their different ideas. Many of the main issues and basic questions in the area can only be solved by combining the different strengths and the different points of view which people are using in studying this topic.

The topics would be divided into four connected subareas:

Generically stable types, their topology, generalizations to generically stable Keisler measures, and their behavior both inside and outside dependent theories.

Non forking outside stable theories, the relation with invariant measures and with the ideals used in Hrushovski's proof of the non commutative Freiman theorem. Aspects of model theory which are useful in additive combinatorics.

Classification theory of unstable theories, with emphasis in dependent theories. The characterizations proved by Shelah, the structure of the externally definable sets, and the role of non forking in all of these ideas. The behavior of non forking both in dependent theories and in generalizations such as NTP2.

The relation in strongly dependent theories between burden, dp-rank, and VC-density.

We have already mentioned multiple aspects of the timeliness for having such a meeting in the near future is perfect. We would also like to mention that there are quite a few young researchers and postdocs who are very active in the area as well as established and influential model theorists and Banff would provide a perfect setting in order to achieve the interaction and collaboration adequate for developing this very interesting area. We believe a workshop of 40 people would be the right size to have most experts attend, as well as postdocs and advanced graduate students.