Advances on Combinatorics of the Real Line and Topology
| Project/Area Number |
23K03198
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12030:Basic mathematics-related
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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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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2025: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2024: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | Real line / Cardinal characteristics / Strong measure zero / Forcing Theory / Ideals on N / Real line combinatorics / Forcing theory / Strong measure zero sets / Ideals / Measure and category |
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| Outline of Research at the Start |
The objective of this research proposal is to continue the research trend motivated by Cichon’s maximum and solve many open problems related to classical combinatorial properties of the real line. We also focus on strong measure zero sets and ideals on the natural numbers, in particular, we propose a generalization of basic notions in mathematical analysis, and produce tools to solve problems in analysis and topology.
It is expected that our results bring new powerful tools in forcing theory, mathematical analysis and topology, with promising applications in many different areas.
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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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Report
(1 results)
Research Products
(13 results)
