Inverse Spectral Problems for Differential Operators

The lecture will be devoted to inverse problems of spectral analysis for ordinary differential operators.
Inverse spectral problems consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics and have many applications in natural sciences. Inverse problems also play an important role in solving nonlinear evolution equations in mathematical physics.
The goal of the lecture is to present the main results in this area and describe the corresponding methods. We will pay the main attention to the so-called method of spectral mappings which is the most effective and universal tool for studying nonlinear inverse problems considered.