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SUMMARY:Motion\, monodromy and asymptotics: Rothschild Lecture - Nalini Jo
 shi (University of Sydney)
DTSTART:20221026T150000Z
DTEND:20221026T160000Z
UID:TALK184178@talks.cam.ac.uk
DESCRIPTION:Felix Klein said that the study of new transcendental function
 s defined by differential equations was "the central problem of the whole 
 of modern mathematics". The same impetus drove the search that led to diff
 erential equations called the Painlev&eacute\; equations\, more than a cen
 tury ago. The subtle properties of their solutions are still being discove
 red and new applications are growing in physics. The solutions of the disc
 rete Painlev&eacute\; equations show tantalizingly similar properties\, bu
 t the study of these transcendental functions remains far from complete.\n
 In this talk\, I will give an overview of three major mathematical threads
  in this area\, which starts with dynamics of planets\, the study of linea
 r differential and difference equations\, and gives a glimpse of the geome
 try underlying these alluring equations. At the end\, I will briefly menti
 on some new work with Pieter Roffelsen (Sydney) on the solutions of the q-
 discrete version of the sixth Painlev&eacute\; equation.
LOCATION:Seminar Room 1\, Newton Institute
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