### Scattering theory for unitary operators

Graduate School of Mathematics

Serge RICHARD

2023 Spring

Mathematics, established in Ancient Greece as a scholarly language with a strict system, was first consolidated in Euclid's “Theorems”. Then, by making mathematics its fundamental language, Physics became a modern science. With the establishment of calculus, new applications of such mechanics were consolidated in Newton's “Principles”. Then, in the 20th Century, mathematical techniques became more important than ever in every field, from social sciences to humanities. Pure Mathematics continues deep and broad investigation of the numbers and geometries of the world, but at the same time mathematics is also heavily concerned with solutions to mathematical phenomena that occur in other subjects. Most recently, proof was found for the previously unsolved “Fermat's Last Theorem”. This was a groundbreaking success of Number Theory, part of Pure Mathematics. Other results from Number Theory are also being used in order to strengthen internet security. In this way mathematics, with Pure Mathematics at its core, is developing even now with a flexible connection to the wider world.

Our graduate school was founded in 1995 as part of placing more importance on graduate schools, following the independence of mathematics from the other science departments. Its purpose is to pioneer the deepening development of traditional Pure Mathematics, and on that basis promote the increasingly wide field of mathematical science. By equipping students with firmly-mastered wide-ranging mathematical abilities and experience in solving new problems using this knowledge, we nurture talented individuals who can effectively contribute to natural sciences, or more widely, to society. To this end, we offer various extra-curricular training to encourage and emphasize the students' independence and self-reliance. One of the characteristics of our graduate school is the accomplishment of active international research with a focus on young people. This has and always will be the tradition of our Department of Mathematics.

Graduate School of Mathematics

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This course will provide an overview of some classical tools of functional analysis which have been partially developed for quantum mechanics. In particular, an introduction to spectral and scatter ....

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