Inverse Spectral and Scattering Problems

Target group

Inverse problems for differential operators are of the utmost importance in fundamental sciences and in a range of applications, including solutions of different types of partial and pseudo differential equations. We are dealing with inverse spectral and inverse scattering problems, which are both interesting topics on their own and as tools in solving the wide range of linear and nonlinear problems, appearing in natural sciences, economics and industry.

Topic and theme

Firstly, we focus on the spectral and scattering properties of the one dimensional differential operators. These problems are very classical and have been solved (mainly) a long time ago. We discuss in details the spectral properties of the differential operators on the finite and infinite intervals. We discuss solutions of classic inverse spectral problems on the finite intervals and inverse scattering problems on the semi-line and line.

After that we focus on the inverse problems for differential operators on graphs, which became of great importance because of the wide range of applications in nanophysics, information science etc. We use the fact, that inverse problems on graphs are locally 1D and it is natural to try to employ the technics used for solving 1D inverse problems. But graphs have a much richer geometry then 1D intervals and as result inverse spectraland scattering problems on graphs are much more elaborated than 1D ones.

Objectives

Participants will learn the major tools of inverse spectral and scattering problems starting from the very classical ones up to the very advanced and they will learn how to apply their knowledge to a wide range of mathematical problems. They will get the first-hand experience in the subject, linking it to their respective research projects. The lectures will be supplemented by the beneficial interactive sessions, problem solving, and interactive learning. Participants will also have an experience of working in groups and learn the logic of the preparation of scientific presentation.

Lecturers

  • Prof. Igor Trushin, Department of Mathematics, Faculty of Sciences , Shinshu University, Japan .

Contact details:

Birth: 22.05.1961-Saratov, Russia.

Education: Saratov University, Russia: 1978-1983, PhD: 1990. Teaching employment: Saratov University, Russia, Associate Professor: 1991-1996, Ewha University, Korea, Visiting Professor: 2002-2003, Chuo University, Tokai University,
Japan, Adjunct professor: 2004-2010, Tohoku University, Japan, Associate Professor: 2010-2019, Shinshu University, Japan, Professor: 2019-present.

Prof Igor Trushin belongs to the group of the leading researchers in the field of inverse and spectral problems. He has authored one book and 23 refereed papers devoted to the topic of these lectures. In addition, he is a referee to the 7 specialized journals for more than 25 years. He is a leading researcher on inverse problems on graphs, linking analytic and geometric methods for the analysis of inverse problems. His deep experience in several related areas will be invaluable for the course participants and other colleagues.

Dates & Programme

  • From Thursday 27 February to Monday 9 March 2020 from 10h00 - 13h00

27/02/2020, Thursday - campus de Sterre, Krijgslaan 281, bld S8 – leslokaal 3.1 (3rd fl)

28/02/2020, Friday - campus de Sterre, Krijgslaan 281, bld S8 – vergaderzaal 3.2 (3rd fl)

02/03/2020, Monday - campus de Sterre, Krijgslaan 281, bld S8 – leslokaal 3.1 (3rd fl)

03/03/2020, Tuesday - campus de Sterre, Krijgslaan 281, bld S8 – vergaderzaal 3.2 (3rd fl)

04/03/2020, Wednesday Lecture  + Interaction class - campus de Sterre, Krijgslaan 281, bld S8 – vergaderzaal 3.2 (3rd fl)

05/03/2020, Thursday Lecture  + Exercise class - campus de Sterre, Krijgslaan 281, bld S8 – leslokaal 3.1 (3rd fl)

06/03/2020, Friday Lecture + Project discussion - campus de Sterre, Krijgslaan 281, bld S8 – vergaderzaal 3.2 (3rd fl)

09/03/2020, Monday Lecture - campus de Sterre, Krijgslaan 281, bld S8 – leslokaal 3.1 (3rd fl)

Registration

https://webappsx.ugent.be/eventManager/events/InverseSpectralandScatteringProblems

Evaluation criteria (doctoral training programme)

active participation: 70%, presentation 30%

Number of participants

15

Maximum 15