Painleve equations and monodromy problems: recent developments

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Workshop theme

Partially supported by the European Community through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652)

This workshop will give a survey of recent developments in Painlevé equations and monodromy problems. Topics to be covered include: Geometry and Painlevé equations; Riemann-Hilbert problems and isomonodromic deformation equations; Painlevé hierarchies; Integrability for discrete equations; Discrete Painlevé equations and applications to orthogonal polynomials; Painlevé equations and random matrix models.

Timetable

Monday 18th September 2006
08:30 to 09:45	Registration	No Room Required
09:45 to 10:00	Opening	Room 1
10:00 to 11:00	Alexander Bobenko Technische Universität Berlin Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green's function	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:30	Painleve systems arising from integrable hierarchies	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Rational surfaces and discrete Painlev\'e equations	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Rodney Halburd Loughborough University Diophantine integrability	Room 1
16:30 to 17:30	Discrete Painleve equations for recurrence coefficients of orthogonal polynomials	Room 1
17:30 to 18:15	Wine and beer reception and poster session	No Room Required
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Tuesday 19th September 2006
09:00 to 10:00	Pierre van Moerbeke Université Catholique de Louvain Critical infinite-dimensional diffusions and non-linear equations for their transition probabilities	Room 1
10:00 to 11:00	Universality of Painleve functions in random matrix models	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	Dissipationless shocks and Painleve equations	Room 1
12:00 to 12:30	Risto Korhonen University of Joensuu Finite order meromorphic solutions and the discrete Painleve equations	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Ilpo Laine University of Joensuu Value distribution of solutions of Painleve differential equations	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Shun Shimomura Keio University A family solutions of a degenerate Garnier system near a singularity	Room 1
16:30 to 17:30	Katsunori Iwasaki Kyushu University The sixth Painleve equation: a chaotic dynamical system	Room 1
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Wednesday 20th September 2006
09:00 to 10:00	Benjamin Doyon University of Oxford Solving Painleve connection problems using 2-dimensional integrable quantum field theory	Room 1
10:00 to 11:00	Dimitri Korotkin Concordia University Bergman tau-function and determinants of Laplacians in flat conical metrics over Riemann surfaces	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	Yoshihiro Murata On matrix Painlev\'e equations	Room 1
12:00 to 12:30	Serguei Barannikov Athens University of Economics and Business TBA	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Informal discussions	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 17:30	Informal discussions	Room 1
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Thursday 21st September 2006
09:00 to 10:00	John Harnad Université de Montréal Matrix integrals as isomonodromic tau functions	Room 1
10:00 to 11:00	Peter Clarkson University of Kent Rational solutions and associated special polynomials associated for the Painlev\'e equations	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	Misha Feigin University of Glasgow Degenerate Gaussian Unitary ensembles and Painlev\'e IV	Room 1
12:00 to 12:30	Hironobu Kimura Degeneration and symmetry of the Schlesinger system from the point of view of Twistor theory	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 14:30	Man Yue Mo The Riemann-Hilbert approach to the asymptotics of isomonodromic problems	Room 1
14:30 to 15:00	Yik-Man Chiang Hong Kong University of Science and Technology Estimates of difference operators in the complex plane	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Marta Mazzocco University of Manchester The Hamiltonian structure of the second Painlev\'e hierarchy	Room 1
16:30 to 17:30	Twistors and monodromy	Room 1
19:30 to 18:00	Conference Dinner in the Old Library at Emmanuel College	No Room Required

Friday 22nd September 2006
09:00 to 10:00	Boris Dubrovin On oscillatory behaviour in PDEs and certain Painleve'-type transcendents	Room 1
10:00 to 11:00	Bernard Malgrange Non-linear differential Galois theory	Room 1
11:00 to 11:30	Coffee	No Room Required
11:30 to 12:00	From the KP hierarchy to the Painlev\'e equations	Room 1
12:00 to 12:30	Vasilisa Shramchenko University of Oxford Riemann-Hilbert problems associated with Hurwitz Frobenious manifolds	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
14:00 to 15:00	Ian Strachan University of Glasgow Two constructions for the isomonodromic tau-functions	Room 1
15:00 to 15:30	Tea	No Room Required
15:30 to 16:30	Alexander Veselov Loughborough University Monodromy-free Schrodinger equations and Painlev\'e transcendents	Room 1
16:30 to 16:45	Closing	Room 1
18:30 to 19:30	Dinner at Selwyn College (Residents only)	No Room Required

Speakers

Serguei Barannikov
Alexander Bobenko Technische Universität Berlin
Yik-Man Chiang Hong Kong University of Science and Technology
Peter Clarkson University of Kent
Benjamin Doyon University of Oxford
Boris Dubrovin
Misha Feigin University of Glasgow
Rodney Halburd Loughborough University
John Harnad Université de Montréal
Katsunori Iwasaki Kyushu University
Hironobu Kimura
Risto Korhonen University of Joensuu
Dimitri Korotkin Concordia University
Ilpo Laine University of Joensuu
Bernard Malgrange
Marta Mazzocco Chennai Mathematical Institute
Man Yue Mo
Yoshihiro Murata
Shun Shimomura Keio University
Vasilisa Shramchenko University of Oxford
Ian Strachan University of Hull
Pierre van Moerbeke Université Catholique de Louvain
Alexander Veselov Loughborough University

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Painleve equations and monodromy problems: recent developments

Workshop theme

Timetable

Speakers

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