Head of Group and Reader in Mathematics, Dr Clare Dunning, from the School of Mathematics, Statistics and Actuarial Science (SMSAS) at the University of Kent, presented a plenary talk at the Seventh Annual Meeting of the Australian and New Zealand Association of Mathematical Physics (ANZAMP) in Merimbula, Australia.
Clare presented a talk titled, ‘Wronskian Hermite Polynomials and the Excited-state ODE/IM Correspondence’.
Wronskian determinants of classical orthogonal polynomials have a number of applications in mathematical physics. For example, they are: building blocks of certain rational solutions of the Painleve equations; the main classes of examples of exceptional orthogonal polynomials; certain solutions of the Kadomtzev-Petviashvili hierarchy of partial differential equations in integrable systems. I will describe how Wronskian Hermite and Wronskian Laguerre determinants describe the excited-state ordinary differential equation/integrable model correspondence at the free-fermion point of the sine-Gordon model. We classify the set of allowed Wronskians and describe some interesting properties of the distribution of their zeros, the latter being one of the open mathematical questions concerning Wronskian determinants of classical orthogonal polynomials.
For more information about the event, visit the ANZAMP website.