CSUN Algebra, Number Theory, and Discrete Mathematics Seminar

Languages, Alphabets, and Group Theory

Gizem Karaali
Pomona College

Wednesday    28 April 2021    3:00 pm–4:00 pm
via Zoom meeting

Abstract: In 1993, J.-F. Mestre, R. Schoof, L. Washington, and D. Zagier defined and explicitly characterized the homophonic quotient groups for French and English. The homophonic quotient of an alphabet-based language in this context is the quotient of the free group generated by the alphabet of the language determined by relations representing standard pronunciation rules. In this talk I will describe how my colleagues Herbert Gangl and Woohyung Lee, and I, native speakers of three quite different languages, applied the methodology proposed in 1993 to our three language systems: German, Korean, and Turkish. Then together with a Swedish mathematician, Per Back, we extended our results to Swedish. Overall, our results point to some interesting differences between these languages (or at least their current script systems). An overview of the algebraic theory of languages will be included, as well as a brief philosophical discussion of the implications of these results.