Title: Somos Sequences - Past and Present
Speaker: Emilie Hogan, Rutgers University
Date: Wednesday, April 20, 2011 12:10pm
Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ
In this talk I will introduce the famed Somos sequences: integer sequences produced by rational recurrences. After Michael Somos introduced these recurrences and sequences, the research area took off. Many people found related recurrences and developed techniques to prove integrality. I will first talk about the three types of proofs that were used to prove integrality of the original Somos sequences. Then I will talk about a recurrence, inspired by Somos, that I discovered with Paul Heideman at University of Wisconsin - Madison while working with Jim Propp. Finally, I will talk about recurrences that surprisingly generate rational numbers (when complex numbers are expected) that I have studied as part of my thesis.