2023 Fiscal Year Research-status Report
Advances on Combinatorics of the Real Line and Topology
| Project/Area Number |
23K03198
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| Research Institution | Shizuoka University |
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Principal Investigator |
メヒア ディエゴ 静岡大学, 理学部, 准教授 (70777961)
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| Project Period (FY) |
2023-04-01 – 2027-03-31
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| Keywords | Real line / Cardinal characteristics / Strong measure zero / Forcing Theory / Ideals on N |
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| Outline of Annual Research Achievements |
This project is focused on four main topics: 1. Forcing models of combinatorics of the reals, 2. Combinatorics of strong measure zero sets, 3. Cardinal characteristics of strong measure zero sets, 4. Combinatorics of the reals modulo the natural numbers. The results of 2023 include two accepted publications in connections with 1. and 4., and several invited talks about advances in 1.-4.. The researcher spent 6 months as an invited professor at TU Wien (Austria), where he presented his results at the University of Vienna (Austria), TU Kosice and Pavol Josef Safarik University (Slovakia) and Wroclaw University (Poland). The intensive research work with members of these universities resulted in great advances in the objectives with several submitted papers and work in progress. A mini-course of 6 lectures about the advances in 1. was offered at the University of Vienna during the winter semester.
The researcher also offered two lectures in Mexico: at the Iberoamerican and Pan Pacific International Conference on Topology and its Applications, and the 56th National Congress of the Mexican Mathematical Society. In the latter event, the researcher advertised education and research in Japan, offering an invitation to graduate students and researchers to study and work in Japan.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The intensive work during the visit to Europe guaranteed great advances in all the four main topics of the project, reflected in the many invited talks. There is a lot of work in progress that will lead many results for the year 2024.
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| Strategy for Future Research Activity |
In 2024 the researcher plans to continue the work started in the previous year, under collaboration with researchers from the University of Vienna, TU Wien, Pavol Josef Safarik University (Slovakia) and the Hebrew University of Jerusalem. It is expected to have publications (or preprints at least) about results in the four main topics of the project.
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