Professor Peter Clarkson (SMSAS) led a successful proposal for a SQuaRE (Structured Quartet Research Ensembles) research program at the American Institute of Mathematics, San Jose, CA together with Percy Deift (New York University, USA), Alexander Its (Indiana University-Purdue University Indianapolis, USA), Nalini Joshi (University of Sydney, Australia), Victor Moll (Tulane University, New Orleans, USA) and Tom Trogdon (University of California, Irvine, USA).

The program will take place at the American Institute of Mathematics, in February 2019. The topic of the program is “The Painleve Project” and the objective is to develop the research done by Peter Clarkson on Painleve equations which formed the basis for the SMSAS Impact Case “Public access to mathematical functions” in REF 2014.

The six Painleve equations were first discovered by the French Mathematician Paul Painleve, who later became Prime Minister of France, and colleagues in the late 19th and early 20th centuries. In recent years the Painleve equations have emerged as the core of modern special function theory.

In the 18th and 19th centuries, classical special functions such as the Bessel, Airy, Legendre, and hypergeometric functions were studied in response to the problems of the day in electromagnetism, acoustics, hydrodynamics, elasticity and many other areas. Around the middle of the 20th century, as science and engineering continued to expand in new directions the Palnleve functions, appeared in applications. The list of problems now known to be described by the Palnleve equations is large, varied and expanding rapidly.