University Seminar: Logic Across Disciplines

Fall 2018

Title: Homotopy Type Theory, the confluence of logic and space
Speaker:  Tslil Clingman, Johns Hopkins University
Date and Time:  Friday, November 30, 3:30-4:30PM
Place: Phillips Hall (801 22nd Street), Room 736

Abstract:  In this talk we will learn how to express ourselves in the language of Homotopy Type Theory and see how it is represents the natural merging of logic and space. We will take some time to consider how identity types, and in particular univalence, free us from certain artificial restrictions of classical logic(s) and foundational systems and give rise to a rich and pleasing theory. Time permitting, we will discuss the role of Univalent Foundations and how Homotopy Type Theory in particular may be leveraged as a foundational system to the direct advantage of the working mathematician.

Title: Relatively C-categorical structures
Speaker:   Valentina Harizanov, GWU
Date and Time:  Friday, November 2, 1-2PM
Place: Rome Hall (801 22nd Street), Room 771

Abstract:  For a computability-theoretic complexity class C, we say that a computable structure A is relatively C-categorical if for every isomorphic structure B, there is an isomorphism that is of complexity C using the atomic diagram of B as an oracle. This notion is more general than C-categoricity and can be expressed syntactically using nice Scott families of formulas. We will give examples from familiar classes of structures and survey recent related results.

Title:  Limit computably categorical structures
Speaker:   Valentina Harizanov, GWU

Date and Time:  Friday, October 26 2018, 01:00pm-02:00pm
Place: Rome Hall (801 22nd Street), Room 771

AbstractWe say that a computable structure is limit computably categorical if for every isomorphic computable structure there is an isomorphism that is computable in the halting set. This notion can be further generalized, and there is a natural connection with definability using computable infinitary formulas. We will investigate limit computably categorical structures from some familiar classes, although such characterization is not known even for linear orders, trees of finite height, equivalence structures, or abelian p-groups.

Title:  Degree Structure of Effective Boolean Algebras
Speaker:   Rumen Dimitrov, Western Illinois University
Date and Time:  Friday, October 12 2018, 01:00pm-02:00pm
Place: Rome Hall (801 22nd Street), Room 771

Abstract: We establish degree embedding results for:  (1) Subalgebras of effective Boolean algebras, and (2) Lattices of subalgebras of effective Boolean algebras. The talk is based on joint work with V. Harizanov and A. Morozov.

Title:  The Algorithmic Complexity of Detecting Group Properties
Speaker:   Iva Bilanovic, GWU, GWU
Date and Time:  Friday, September 28 2018, 01:00pm-02:00pm
Place: Rome Hall (801 22nd Street), Room 771

Abstract: We consider the question: from a “nice” description of a group, can we detect whether or not it has some property of interest? Our nice descriptions will be recursive presentations and computable atomic diagrams. We show that for classes of groups with such descriptions, the detection of a Markov property is not computable. Then we look at some specific properties of high computability theoretic complexity. This will be a more technical continuation of my previous talk, but all necessary background material will be presented. 

Title:  Decision Problems and Groups
Speaker:   Iva Bilanovic, GWU
Date and Time:  Friday, September 7 2018, 01:00pm-02:00pm
Place: Rome Hall (801 22nd Street), Room 771

Abstract:  We will discuss decision problems, those that can be formulated as yes/no questions of the inputs, and how to determine the algorithmic complexity of a procedure that makes such decisions. Computable functions, the Kleene-Mostowski arithmetical hierarchy of sets, and other related notions and topics will be discussed at length. In the final portion of the talk, we will turn our attention to decision problems both for recursively presented and for computable groups.

Title:  Multiplying Fractions in a Topological Way
Speaker:   Jozef Przytycki, GWU -
Date and Time:  Friday, September 21 2018, 01:00pm-02:00pm
Place: Rome Hall (801 22nd Street), Room 771

Abstract:  TBA