University Seminar (CCAS): Computability, Complexity, and Algebraic Structure

Time: Wednesday, October 18, 11:15am – 12:15pm

Place: Monroe Hall, Room 250

Speaker: Michael Somos, Catholic University of America

Title:  Somos sequences: then and now

Abstract:  The Somos sequences are a family of rational number sequences defined by simple rational recurrences. The first four are unexpectedly integer sequences. This is because those recurrences produce Laurent polynomials while the rest do not. This “Laurent phenomenon” is a special case of Cluster Algebras. The origin of Somos sequences was to model Jacobi theta functions using integer sequences similar to how Fibonacci/Lucas sequences model trigonometric functions. This is more fully developed in my “WXYZ Math Project.” Elliptic divisibility sequences are a special case of generalized Somos-4 sequences. Somos sequences have applications to solving Diophantine equations. They appear in a special case of Hankel Number Walls.