Undergraduate Mathematics Day 2023

Abstract: In 1960 Eugene Wigner wrote a now-famous article titled The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In 1993, the homophonic quotient groups for French and English (the quotient of the free group generated by the French (respectively English) alphabet determined by relations representing standard pronunciation rules) were explicitly characterized. In this talk, we will explore the mathematical and philosophical connections between these two works. Mathematically I will describe how my colleagues Herbert Gangl, Woohyung Lee (PO'15) and I, native speakers of three quite different languages, applied the methodology proposed in 1993 to our three language systems: German, Korean, and Turkish. Our results point to some interesting differences between these three languages (or at least their current script systems). An overview of the algebraic theory of languages will be included, as well as a philosophical discussion of the implications of these results.

Gizem Karaali is originally from Istanbul, Turkey, where she received undergraduate degrees in electrical engineering and mathematics. She got her Ph.D. in mathematics from the University of California Berkeley. She is currently a professor of mathematics at Pomona College. She is a founding editor of the Journal of Humanistic Mathematics and a senior editor of Numeracy, the journal of the National Numeracy Network. Karaali has published over a hundred articles as well as four edited volumes; most recently she edited, with Lily Khadjavi, the 2021 MAA Press book Mathematics and Social Justice: Focusing on Quantitative Reasoning and Statistics, which followed a 2019 book titled Mathematics and Social Justice: Resources for the College Classroom. In the last decade, Karaali received federal grants for her research and teaching (from the National Security Agency and the National Endowment for the Humanities).

Abstract:  Cryptography is the study of hidden information.  This includes techniques to create and read secure secret messages (encryption/decryption) as well as methods to break the security of hidden messages, regardless of the intended recipient (cryptanalysis).  This talk will explore basic cryptographic principles using manual cryptosystems, progress to the concepts behind - and the mechanical inner workings of - the well-known Enigma Cipher deployed in WWII, and discuss how cryptography surrounds us in the modern day.

Frank Casabianca is the National Security Agency (NSA) Visiting Professor at the US Military Academy at West Point.  He earned his bachelor’s degree in mathematics at the University of Florida and Ph.D. at Auburn University.  His 20-year career at NSA includes a variety of assignments in Signals Intelligence and Cybersecurity.  Frank has interests in group theory, combinatorics, and recreational math, in addition to cryptography and national security issues.