## Topics in Analytic Theory of Differential Equations

### Prof. Boris Dubrovin

- Movable and fixed singularities of solutions of ODEs in complex domain. Equations of Painleve' type.
- Monodromy of linear ODEs with rational coefficients. Stokes phenomenon.
- Monodromy "in large" and braid groups.
- Moduli of linear ODEs with rational coefficients with given monodromy (monodromy preserving deformations): analytic structure, geometry, hamiltonian formalism.
- Invanriants of discrete groups and particular solutions of equations of Painleve' type.
- Applications to differential equations of topological field theory.