University Seminar: Logic Across Disciplines

Fall 2019

Title: Markov properties
Speaker: Iva Bilanovic, GWU
Date and time: Friday, October 11, 11:00am-12 noon
Place: Phillips Hall (801 22nd Street), Room 736

Abstract: We begin with a historical treatment of Markov properties in the original context of recursively presented groups and their relation to early questions in computability theory. We will then abstract the notion to other classes of structures and, time allowing, consider the examples of partial injection structures and nested equivalence classes.


Title: Motivating and characterizing large cardinals
Speaker: Philip White, GWU
Date and time: Friday, October 4, 11:00am-12 noon
Place: Phillips Hall (801 22nd Street), Room 736

Abstract: There are certain properties which characterize the largeness of N. Whether or not these same features of largeness can be applied to an uncountable cardinal aleph is independent of the traditional axioms of set theory. If we suppose there exists a large cardinal exhibiting such features, we arrive at a theory provably stronger than traditional set theory. The aim of the talk is to motivate large cardinals as well as to introduce a preliminary result involving a new large cardinal notion (obtained under the guidance of Brent Cody of VCU).


Title: Forcing, an introduction
Speaker: Philip White, GWU
Date and time: Friday, September 27, 11:00am-12 noon
Place: Phillips Hall (801 22nd Street), Room 736

Abstract: Forcing is a mathematical technique developed by Paul Cohen in the 1960s, which he used to prove the independence of the continuum hypothesis. Although forcing in many ways has become the standard technique used in set theory, to non-set-theorists it often seems like a mystery. We hope to give a quick introduction to the forcing technique, all the while making the technique seem less enigmatic to the non-set-theorist.


Logic-Topology Seminar

Title: Gram determinants and Temperley-Lieb algebras
Speaker:  Jozef Przytycki, GWU, http://home.gwu.edu/~przytyck/
Date and Time:  Friday, September 20, 11:00AM-12:00PM
Place: Phillips Hall (801 22nd Street), Room 736

Abstract:  I will outline research completed with my students Rhea, Dionne, and Sujoy as part of our Mathathon IV project (December 2018-May 2019). We worked on Gram type determinants motivated and applied to Knot Theory. In particular, we found the closed formula involving Chebyshev polynomials for a Gram determinant involving the trace of Temperley-Lieb algebra.


Title: Can you always raise a natural number to a power? (Part 2)
Speaker:  Keshav Srinivasan, GWU
Date and Time:  Friday, September 13, 11:00AM-12:00PM
Place: Phillips Hall (801 22nd Street), Room 736

Abstract:  We will continue our discussion of predicativity, the notion that we can only define new mathematical objects in terms of existing mathematical objects.  We will walk through the proofs of results by John Burgess and Allen Hazen, concerning how much of natural number arithmetic can be recovered in predicative second-order logic. In the final part of the talk, we will discuss potential avenues for future research extending Burgess’ and Hazen's work.


Title: Can you always raise a natural number to a power?
Speaker:  Keshav Srinivasan, GWU
Date and Time:  Friday, September 6, 11:00AM-12:00PM
Place: Phillips Hall (801 22nd Street), Room 736

Abstract:  We will discuss predicativity, the notion that we can only define new mathematical objects in terms of existing mathematical objects.  We will give an introduction to second-order logic, and explain how we can use it to do mathematics predicatively.  In the final portion of the talk, we will discuss work by John Burgess and Allen Hazen concerning how much of Peano arithmetic is predicatively justifiable.

 

 

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