Analytic aspects of the theory of Monodromy preserving deformations of linear ordinary differential equations with rational coefficients have been studied since the beginning of the century, especially in connection with the `Painlevé property' of completely integrable systems. Recently, a geometric understanding of the structure of the parameter spaces of the deformations has emerged. In particular, the structure of a Frobenius manifold was discovered on the space of isomonodromic deformations of certain special systems of first order linear differential equations.

The lectures of Professor Dubrovin will explain how the geometry of Frobenius manifolds connects the theory of isomonodromic deformations with the (topological) quantum field theory associated to Gromov - Witten invariants for symplectic manifolds and with the bihamiltonian geometry of loop spaces.

There will also be the following additional seminars:

Prof N.J.Hitchin (Oxford) Isomonodromic Deformations and Self-Dual Metrics,
Prof A.P.Veselov (Loughborough)  Deformation of root systems and new solutions to the
                                                                     generalised  WDVV equations,
Dr N.M.J.Woodhouse (Oxford) Twistor theory and isomonodromy.

The programme will consist of two lectures by Professor Dubrovin each day,  with additional seminars and classes  for research students on  the Tuesday, Wednesday and Thursday.  Registration will start at 2.30pm on the Monday and the last lecture will finish before lunch on the Friday.

There is no registration fee, but those wishing to  attend are asked to register by e-mail to  lmason@maths.ox.ac.uk .

The lectures and classes will all take place in the Mathematical Institute, Oxford.   Travel information can be found here.

Board and lodging can be arranged at St Peter's College for the duration of the Lecture Series.
 Click here for further details about board and lodging.

Some financial support is available for UK participants.

Please address all enquiries by e-mail to Lionel Mason: lmason@maths.ox.ac.uk