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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Isomonodromy and integrability - Previato\, E (Bos
ton)
DTSTART;TZID=Europe/London:20090630T090000
DTEND;TZID=Europe/London:20090630T100000
UID:TALK18956AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18956
DESCRIPTION:The property of having no movable critical points
for an ordinary differential equation was linked w
ith integrable systems via theta functions in the
19th century\, and more recently\, since the 1970s
\, with integrable partial differential equations
via similarity reduction. A geometric integration
of these features will be explored in the first pa
rt of the talk\, after work by H. Flaschka (1980)\
, which suggests a deformation of the spectral cur
ve. This provides the segue to the second part of
the talk\, concerning a joint project with F.W. Ni
jhoff. The isomonodromy equations for spectral dat
a (e.g.\, the Baker function) are studied as syste
ms of ODEs\, following R. Garnier (1912). Special
functions\, specifically the Kleinian sigma functi
on\, are implemented in the equations\, to seek th
e Gauss-Manin-connection counterpart of the Legend
re equation\, by which R. Fuchs (1906) had connect
ed the isomonodromy property and the absence of mo
vable critical points. Work by Nijhoff et al. on d
iscrete and Schwarzian equations would be related
to this higher-genus Legendre version of the isomo
nodromy condition.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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