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SUMMARY:Isomonodromy and integrability - Previato\, E (Boston)
DTSTART:20090630T080000Z
DTEND:20090630T090000Z
UID:TALK18956@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The property of having no movable critical points for an ordin
 ary differential equation was linked with integrable systems via theta fun
 ctions in the 19th century\, and more recently\, since the 1970s\, with in
 tegrable partial differential equations via similarity reduction. A geomet
 ric integration of these features will be explored in the first part of th
 e talk\, after work by H. Flaschka (1980)\, which suggests a deformation o
 f the spectral curve. This provides the segue to the second part of the ta
 lk\, concerning a joint project with F.W. Nijhoff. The isomonodromy equati
 ons for spectral data (e.g.\, the Baker function) are studied as systems o
 f ODEs\, following R. Garnier (1912). Special functions\, specifically the
  Kleinian sigma function\, are implemented in the equations\, to seek the 
 Gauss-Manin-connection counterpart of the Legendre equation\, by which R. 
 Fuchs (1906) had connected the isomonodromy property and the absence of mo
 vable critical points. Work by Nijhoff et al. on discrete and Schwarzian e
 quations would be related to this higher-genus Legendre version of the iso
 monodromy condition.\n
LOCATION:Seminar Room 1\, Newton Institute
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