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Resources

This conference deals with connections between two distinct areas of mathematics: Model Theory and Operator Algebras. We anticipate a number of participants that are experts in both areas, as well as many participants that work primarily in one area but are interested in learning more about the other, and several graduate students. For anyone who wished to learn more about either area, we're providing some resources that will be useful throughout the 5-lecture series as well as many of the plenary talks.

Introductory Lecture

Greg Oman will give an introductory lecture providing background on Model Theory.

Title: Introduction to Model Theory with Applications to Algebra

Abstract: We will begin by discussing the syntax and semantics of first-order languages (this talk does not assume any background in logic). We will then discuss some fundamentals of model theory including completeness of theories, compactness, Lowenheim-Skolem Theorems, axiomatizability, and elementary submodels. We will illustrate these ideas through examples taken from some recent papers. In particular, we will work in groups, rings, and fields. Only basic graduate algebra will be required to understand the results presented in this talk.

Model Theory References

• Model theory for metric structures, I. Ben Yaacov, A. Berenstein, C. W. Henson, and A. Usvyatsov, in Model theory with applications to algebra and analysis. Vol. 2, London Mathematical Society Lecture Note Series 350, 2008.
  
  
• Model theory of operator algebras II: model theory, I. Farah, B. Hart, and D. Sherman, Israel Journal of Mathematics, 201 (2014), no. 1, 477--505.
  
  
• Model Theory of C*-algebras, I. Farah, B. Hart, M. Lupini, L. Robert, A. Tikuisis, A. Vignati, and W. Winter, preprint (2016).
  
  
• Enforceable operator algebras, I. Goldbring, preprint (2017).
  
  

Operator Algebra References

• The following book is perhaps not the best for learning the subject, but it does serve an excellent encyclopedia. You may wish to refer to it throughout the conference and look up any operator algebra concepts you wish to learn more about.
  
  Operator Algebras: Theory of C*-algebras and von Neumann Algebras by Bruce Blackadar
  
• Notes from an introductory course on C*-algebras by Dana Williams:
  
  Lecture Notes on C*-algebras
  
• This is a note written by Ilijas Farah based on two talks given by Efren Ruiz at the Toronto Set Theory seminar in November 2005.
  
  C*-algebras and their representations
  
• These are two commonly used textbooks for a first course in C*-algebras.
  • C*-algebras and Operator Theory by Gerard J. Murphy. (You can find an incomplete copy viewable on Google Books.)
  • C*-algebras by Example by Kenneth R. Davidson.