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Clocks, Parking Garages, and the Solvability of the Quintic: A Friendly Introduction to Monodromy

Imagine the hands on a clock. For every complete rotation the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way. We may think of the hour hand as generating a group such that when we "move" twelve times then we get back to where we started. This is the elementary concept of a monodromy group.

In this ICMS Public Lecture, Edray Goins gives a gentle introduction to a historical mathematical concept which relates calculus, linear algebra, differential equations, and group theory into one neat theory called "monodromy". He'll explore lots of real world applications, including why it's so easy to get lost in parking garages, and present some open problems in the field. He'll end the talk with a discussion of how this is all related to solving polynomial equations, such as Abel's famous theorem on the insolubility of the quintic by radicals.

Edray Herber Goins is Professor of Mathematics at Pomona College. He has worked as a researcher at both Harvard and the National Security Agency; and has taught at both Caltech and Purdue. Professor Goins has published over 20 journal articles in areas such as applied mathematics, graph theory, number theory, and representation theory; and on topics such as Diophantine equations, elliptic curves, and African Americans in mathematics. He has acted as a referee for 20 different journals in mathematics, served on dozens of panels for the National Science Foundation, and has given more than 150 invited addresses on his research.