2010 photo 

C. Ward Henson

Professor Emeritus
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street, Urbana, Illinois 61801-2975 USA.
professional email: cwhenson(at)illinois(dot)edu -- new in early 2018;
     ("old" addresses w-henson(at)illinois(dot)edu and henson(at)math(dot)uiuc(dot)edu will also    
      work; they are treated as aliases, and mail to either of them will be appropriately forwarded.)
personal email: cwhenson(at)gmail(dot)com
home address and phone: 2925 Lincoln Way, San Francisco, California 94122; +1-415-661-4559

Selected Slides from Recent Talks by Henson:

Slides for a talk given in November 2019 at Notre Dame and the University of Illinois (Urbana) on Model theory of R-trees and of ultrametric spaces.  (Slides last revised on 11-14-2019.)

Updated slides from a 2019 talk on Ultraproducts as a tool in the model theory of metric structures, given in several places. (Slides last revised on 4-23-2020.)  A subset of these slides were used for a 4-22-2020 zoom seminar "at" Cornell.)
This mostly expository talk lays out how understanding ultraproducts of members of a class C of metric L-structures can be an important practical tool for understanding the full class of models of  the theory of C -- including not only the models themselves, but also the definable predicates and (especially) definable sets in those models, and often also toward getting an explicit set of axioms for that theory. Ultraproducts have proved to be much more important in the model theory of structures from functional analysis and geometry than in classical model theory of discrete, algebraic structures.  There are several examples at the end, including an aspect of the speaker's program with Yves Raynaud to verify many new examples of uncountably categorical Banach spaces.  The basic tools discussed here were developed in conversations with Bradd Hart and Isaac Goldbring.  For basic background and some proofs of definability results, see:
             BenYaacov, Berenstein, Henson, Usvyatsov; Model theory for metric structures, Section 9, published in 2008.
             Goldbring, Spectral gap and definability, section 2; preprint 2018.   
             Hart, slides for talks at ASL annual meeting and BIRS workshop in 2018.

Slides for a 2019 talk on Uncountably Categorical Banach Spaces, with some new examples (joint work with Yves Raynaud).

Slides for a talk given on Oct. 2, 2018, in Notre Dame's logic seminar, entitled "On the model theory of group actions on probability measure spaces".  This is based on a collaboration with Alex Berenstein.  The talk was also given in Urbana's model theory seminar on Sept. 28, 2018.

Slides for a talk in the logic seminar at Notre Dame on April 18, 2017 are linked here.  The title is Uncountably Categoricity for Structures Based on Banach Spaces and the main new results have to do with examples of uncountably categorical Banach spaces that have been constructed/verified in joint work with Yves Raynaud, Univ. of Paris 6.  A paper by Henson and Raynaud has been published in Commentationes Mathematicae and is available as arxiv:1606.03122.  Talks were given at earlier stages of the project in Lyon, France, at UCLA, and at a Midwest Model Theory Day at UIC.  In the background is a weak form of a theorem of
Baldwin-Lachlan, for classical structures, that has been proved for Banach structures by Shelah and Usvyatsov, in which Hilbert space plays a role analogous to that of a strongly minimal set.

Slides for a talk given in a Special Session on Continuous Model Theory at the ASL Annual Meeting, March 20-23, 2017, at Boise State University, are linked here.  The title is Continuous model theory, and the purpose was to provide some background for the other talks in that special session.  The slides contain about twice the material that could be presented in the talk, and also give a short list of references at the end.

Slides for talks given in Paris (Analysis Seminar, Nov. 12, 2015) and in Berkeley (Model Theory Seminar, Nov. 18, 2015) are linked here.  The title is Banach lattice methods for proving axiomatizability of Banach spaces.  The talk discussed new methods based on a study of disjointness preserving linear isometries between Banach lattices, introduced by Raynaud, and a main theorem proved first by Raynaud and then strengthened by Henson.  This is part of an ongoing collaboration.

LOGIC AND MATHEMATICS 2011: this conference took place September 3-4, 2011, at UIUC.  Invited speakers were Itai Ben Yaacov (Lyon), Gregory Cherlin (Rutgers), Julien Melleray (Lyon), Anand Pillay (Leeds), Christian Rosendal (UIC), David Sherman (Virginia), and Henry Towsner (UCLA).  For more information, including the titles of talks and abstracts, look HERE.

Research Interests of CWH:

Articles on continuous first-order logic and the model theory of metric structures:

This page was last modified on April 23, 2020.