Applications of singularity theory to other fields
| Reference No. | 20200025 |
|---|---|
| Type/Category | Grant for Young Researchers- Short-term Visiting Researcher |
| Title of Research Project | Applications of singularity theory to other fields |
| Principal Investigator | Yutaro Kabata（Faculty of Information and Data science, Nagasaki University・Assistant Professor） |
| Research Period |
November 4,2021. ～
November 5,2021. March 16,2022. ～ March 18,2022. |
| Keyword(s) of Research Fields | Singularity theory, Life science, Image processing, Statistics |
| Abstract for Research Report |
Focusing on the singularities and singularities of functions and maps (or families of submanifolds derived from them) is also common in the natural sciences and engineering. For example, some feature points of image processing, such as ridge points, are derived from certain kinds of singular points on surfaces and are very useful for practical use. On the other hand, it is not easy for non-experts to handle the properties of functions and maps, and their analysis in various areas remains relatively simple or typical. Moreover, even if a mathematics expert is engaged in applied research, he or she is often satisfied with the existing framework by directly applying it to other fields just from his or her mathematical?interests. In this proposal, applicants who are experts in singularity theory will stay at Kyushu University as short-term researchers and discuss with researchers in various fields. The purpose is to help researchers in different disciplines understand the perception of the problem and pave the way for the formulation of the complex characteristics they face in that discipline. At the same time, it aims to clarify the elements lacking in the existing theory in the practice of singularity theory. This proposal at least clarifies the problem of new applications in singularity theory and geometry. As a future result, we can expect to bring a new framework to the singularity theory inspired by applied problems (as can be seen from the famous Tom and Arnold study, the singularity theory is based on "good applications"). In addition, it can provide interdisciplinary researchers with access to recent singularity and geometry studies. In addition, if a good subject is found in this plan, it will lead to collaborated works. |
| Organizing Committee Members (Workshop) Participants (Short-term Joint Usage) |
Yutaro Kabata（Nagasaki University・Assistant Professor ） |
| Adviser | Shizuo Kaji (IMI, Kyushu University, / Professor) |