Title: Extended Somos and Gale-Robinson sequences, dual numbers, and cluster superalgebras

Date: 04/18/2017

Time: 2:00 PM - 2:50 PM

Place: C304 Wells Hall

In 1980, Michael Somos invented integer sequences that have later been popularized and generalized (among others) by David Gale. A certain mystery around this class of sequences is probably due to their relation with a wealth of different topics, such as: elliptic curves, continued fractions, and more recently with cluster algebras and integrable systems.
I will describe a way to extend Somos-4 and Somos-5 and more general Gale-Robinson sequences, and construct a great number of new integer sequences that also look quite mysterious. The construction is based on the notion of 'cluster superalgebra' (which can be used as a machine to produce integer sequences).
Most of the talk will be accessible to non-experts in any of the above mentioned subjects.