Math seminar by Dr. Shu Nakamura

The iTHEMS Math seminar was held on 23 January, inviting Shu Nakamura from Gakushuin university. The title of the talk was “Semiclassical methods in mathematical quantum mechanics”. The topic was semiclassical analysis and scattering theory of Schrödinger operators.
In the first part, the speaker gave a introductory talk on the microlocal analysis and semiclassical analysis of Schrödinger operators. He started his talk by introducing a canonical quantization. Then he explained how canonical quantization is understood in the framework of semiclassical and microlocal analysis. Moreover he explained some recent results on this research field.
In the second part, the speaker explained his recent results on scattering matrix of Schrodinger operators with long range potentials. At the beginning, he introduced the definition of scattering matrix and some known results. Then he stated his main result on the representation of scattering matrix. As an application, he gave some examples of long range potentials for which he proved several spectral properties of scattering matrix.