**Topics in Analytic Theory of Differential Equations**

**by Prof. Boris Dubrovin**

1. Movable and fixed singularities of solutions of ODEs in complex domain. Equations of Painleve' type.

2. Monodromy of linear ODEs with rational coefficients. Stokes phenomenon.
Monodromy "in large" and braid groups.

3. Moduli of linear ODEs with rational coefficients with given monodromy (monodromy preserving deformations): analytic structure, geometry, hamiltonian formalism.

4. Invanriants of discrete groups and particular solutions of equations of
Painleve' type. Applications to differential equations of topological field theory.