Index theorems in scattering theory: beyond a finite number of bound states

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K03328
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Nagoya University
• Principal Investigator: Richard Serge 名古屋大学, 多元数理科学研究科(国際), G30特任教授 (70725241)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: Scattering theory / Wave operators / Index theorems / Integrable models / Bibliometric analaysis / Epidemiology

Outline of Final Research Achievements

We have developed analytical tools in the context of quantum scattering theory. These results are necessary for exhibiting properties of physical systems which are robust under perturbations. Because of the pandemic, we have also performed bibliometric research on mathematical papers, and developed new tools for computing the effective reproduction number of the COVID-19 epidemic.

Free Research Field

Mathematics

Academic Significance and Societal Importance of the Research Achievements

Stability results of quantum systems are important, since these systems are constantly subject to perturbations. Bibliometric investigations provide a clear link between international collaborations and citations. New methods for computing the effective reproduction number can have a huge impact.