McGill Logic, Category Theory, and Computation Seminar Friday, 20 January 2017 in Leacock 927 (see note below) 3:30 - 5:30 M. Makkai (McGill) Meta-mathematics in Bourbaki's structuralism and in more recent developments in mathematical structuralism [Abstract on webpage] Note: This is not part of this seminar's activities, but may be of interest to our regular participants. Location: The talk will be held in the Dept of Philosophy, McGill, Leacock 927. 24 January 2017 (New starting time!) 3:00 - 4:00 Forte Shinko (McGill) Borel complexity of boundary actions of hyperbolic groups Abstract: An active area of descriptive set theory seeks to compare and classify the complexity of Borel equivalence relations via the notion of Borel reduction. Given a group acting geometrically on a hyperbolic space, we will investigate the Borel complexity of the induced action on the Gromov boundary. This is joint work with Jingyin Huang and Marcin Sabok. 31 January 2017 (Note starting time!) (3pm will continue to be our usual starting time till further notice.) 3:00 - 4:00 Forte Shinko (McGill) Borel complexity of boundary actions of hyperbolic groups II Abstract We will present the proof due to Dougherty, Jackson and Kechris that the tail equivalence relation on 2N is hyperfinite, and then investigate how this proof could be generalized to the setting of hyperbolic groups. 7 February 2017 3:00 - 4:00 Prakash Panangaden (McGill) Logical Characterization of Simulation Abstract I will define simulation for Labelled Markov processes and show that there is a simple modal logic that charaterizes simulation. This was originally proved by Desharnais et al. in 2003 using approximation techniques. Our proof uses descriptive set theory instead and less overall machinery. More importantly, it gives new insight into the relation between logic and simulation. I will also present a "nice" game characterization of simulation and bisimulation. I will explain what "nice" means in this context. This is joint work with Bartek Klin and Nathanaël Fijalkow with one important lemma pointed out to us by Roman Pol. There will be no category theory in this talk. 14 February 2017 3:00 - 4:00 Prakash Panangaden (McGill) Logical Characterization of Simulation II 7 March 2017 3:00 - 4:00 Phillip Wesolek (Binghamton) Elementary amenable groups and the space of marked groups Abstract: The space of marked groups is a compact Polish space that parameterizes all countable groups. This space allows for tools from descriptive set theory to be applied to study group-theoretic questions. The class of elementary amenable groups is the smallest class that contains the abelian groups and the finite groups and that is closed under group extension, taking subgroups, taking quotients, and taking countable directed unions. In this talk, we first give a characterization of elementary amenable marked groups in terms of well-founded trees. We then show the set of elementary amenable marked groups is coanalytic and non-Borel. This gives a new proof of a theorem of Grigorchuk: There are finitely generated amenable non-elementary amenable groups. 14 March 2017 3:00 - 4:00 M Makkai (McGill) First-order logic with dependent sorts (FOLDS) and the related generalization of the concept of isomorphism, "FOLDS equivalence" Abstract: This will be a partial introduction to the subject I first wrote about in 1995 in the monograph with the similar title (see my website). A shorter description is in the (published) 1998 paper no. 68 in my CV (on the website; also downloadable). There are more things on FOLDS on my website, and away from it as well. For instance, the MSC thesis of Christian Boudreault, which is relevant to the specific things I want to say, I still have to put on my website. Although my familiarity with the literature tends to be spotty, I have the long-standing and strong impression that FOLDS and FOLDS equivalences have generated little interest either in the logical or in the categorical community: let this be a warning for you. After generalities, I will concentrate on countable structures, the family of analytic equivalence relations given by FOLDS equivalences, and logical connections, e.g. a generalization of Scott's isomorphism theorem on countable structures. 21 March 2017 3:00 - 4:00 M Makkai (McGill) First-order logic with dependent sorts (FOLDS) and the related generalization of the concept of isomorphism, "FOLDS equivalence" Abstract: I will explain, how the method started, what Eilenberg and Mac Lane used it for, how Harry Appelgate gave it a categorical setting, how Jon Beck and I realized that in our setting it took a simpler form. I will go on with Michael Andre's version and how I began to write a book on the method until two questions from grad student Rob Milson started me off in a different direction that, among other things tied Andre's version together with the older ones. I will likely take two lectures. 4 April 2017 3:00 - 4:00 M Barr (McGill) Acyclic Models - explanation and a brief history II 11 April 2017 3:00 - 4:00 M Barr (McGill) Acyclic Models - explanation and a brief history III 19 September 2017 2:30 - 3:30 Amit Sharma (McGill) A K-theory for symmetric monoidal categories [Abstract on webpage] 26 September 2017 2:30 - 3:30 Amit Sharma (McGill) A K-theory for symmetric monoidal categories II 3 October 2017 2:30 - 3:30 David Spivak (MIT) String diagrams for traced and compact categories are oriented 1-cobordisms [Abstract on webpage] Friday, 20 October 2017 Location: BH1214 2:30 - 3:30 Dana Bartosova (Carnegie Mellon) Questions on freedom of actions [Abstract on webpage] 24 October 2017 2:30 - 3:30 Michael Barr (McGill) Beck modules for a monoid [Abstract on webpage] [Notes for the talk on webpage] 7 November 2017 2:30 - 3:30 Prakash Panangaden (McGill) Quantitative equational logic 21 November 2017 2:30 - 3:30 Joseph Helfer (Stanford) First-order homotopical logic [Abstract on webpage] 5 December 2017 2:30 - 3:30 Jesse Han (McMaster) Strong conceptual completeness for ?0-categorical theories [Abstract on webpage] [Slides on webpage] =================================================== PLACE: BURNSIDE HALL 920, McGILL UNIVERSITY (unless otherwise indicated) =================================================== (Any comments, suggestions to rags@math.mcgill.ca) Seminar listings are available here: http://www.math.mcgill.ca/triples The latest revised details about talks and times are to be found there.