Neostability Theory (15w5145)

Arriving in Oaxaca, Mexico Sunday, July 12 and departing Friday July 17, 2015

Organizers

Bradd Hart (McMaster University)

Ehud Hrushovski (Hebrew University at Jerusalem)

Alf Onshuus (Universidad de los Andes, Edificio H)

(University of Notre Dame)

(University of California at Berkeley)

(Université Claude Bernard Lyon 1)

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 and its consequences on Berkovichifications, 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 and possible applications to statistical learning theory.

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.

This meeting will happen after a model theory semester in MSRI (January through May 2014) and thus, will have an important role in the tying-up and final shaping of ideas. Consequently, we may "twist" some of the areas involved in the meeting if particularly new and interesting ideas come up of the MSRI semester.


The topics will 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. Consequences of understanding Berkovich spaces as topologies on generically stable types.

  • 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. Possible applications to statistical learning theory.