Abelian Functions: New results for functions associated with a cyclic tetragonal curve of genus six
Matthew England (Heriot-Watt)
Tuesday 25th November, 2008 15:00-16:00 Mathematics Building, room 204
This presentation will be on the topic of Abelian (multiply periodic) functions. These functions are defined in analogy to the Weierstrass $\wp$-function, and we use them to generalise some of the elliptic results to higher genus functions. After a review of the lower genus cases I will present some new results for functions associated with a cyclic tetragonal curve of genus six. These include the associated partial differential equations satisfied by the functions, a series expansion for the sigma-function and a new addition formula. I will discuss some applications within the field of integrable systems, demonstrating that such functions can give a solution to the KP-equation and outlining how a general class of solutions could be generated using a wider class of curves.