Neostability Theory (18w5193)

Arriving in Oaxaca, Mexico Sunday, October 14 and departing Friday October 19, 2018

Organizers

(Université Claude Bernard Lyon 1)

Anand Pillay (University of Notre Dame)

Alf Onshuus (Universidad de los Andes, Edificio H)

(University of California at Berkeley)

Objectives

The main objective is to understand what is known and what needs to be done in the fields described above:



  1. Finding more applications of Keisler measures, distality and stability to combinatorics (regularity theorems).
  2. Topological dynamics (for both definable groups and
  3. automorphism groups) and the relation with definably amenable groups. In particular, understanding the relation between amenability of automorphism groups and strong types. Understanding the fefinable topological dynamics of p-adic groups. And finding new invariants of first order theories coming from the topological dynamics of automorphism groups.



  4. Continue to study pseudofinite model theory, with all the different branches described in the State of the Art.




  5. Properties of forking, independence relations, definable
  6. groups in Dependent and NTP$_2$ structures



  7. Foundational work on $NTP_1$ and $n$-dependence.




Besides this, there are two lines of research that right now seem quite promising, and that could have matured even further by 2018. Hrushovski and Ben Yaacov are developing a theory of ``Globally Valued Fields''. Also, Will Johnson characterized fields in dp-minimal structures, defining a topology on any such field. Generalizing this to strongly dependent fields is one of the main challenges within the community.



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.



Finally, 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.