2020 Fiscal Year Research-status Report
Synthesising directed structures in Computer Science using Directed Algebraic Topology
| Project/Area Number |
19K20215
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| Research Institution | National Institute of Informatics |
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Principal Investigator |
DUBUT Jeremy 国立情報学研究所, 大学共同利用機関等の部局等, 特任研究員 (50836765)
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| Project Period (FY) |
2019-04-01 – 2022-03-31
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| Keywords | algebraic topology / topological robotics / concurrent systems / language theory |
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| Outline of Annual Research Achievements |
During the current fiscal year, I have been working on two main directions for the present project.
First, I have been developing the categorical foundations for studying topological robotics with control constraints, which requires to look at new concepts in directed algebraic topology such as components of topologically enriched categories.
Second, I have been developing a categorical theory for the language of general transition systems. The challenge is to be able to deal with probabilistic and truly concurrent behaviours. The target is to have a nice way to describe languages for Higher Dimensional Automata, and their possible extensions with various phenomena such as time or probabilities.
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| Current Status of Research Progress |
Current Status of Research Progress
4: Progress in research has been delayed.
Reason
The research on that project deeply relies on collaboration with Europe. The current global pandemic makes it hard to collaborate with my colleagues (they are very busy with setting up online courses, and managing the sanitarian situation in their universities). Furthermore, trips have been cancelled at the beginning of the fiscal year that would have been real boosts for the project.
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| Strategy for Future Research Activity |
The situation in Europe is improving, and collaborations are starting again. My plan is to finish the two lines I described earlier as soon as possible and to submit papers related to them, one in a mathematical journal, and at a computer science conference.
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| Causes of Carryover |
The reason for the left-over is that this money was primarily intended for trips such as collaborations and conferences. With the current pandemic, these were cancelled or changed as online events. For the next year, I am hoping that the situation will get better so that I can visit (or invite) collaborators to boost the research of this project. I am also planning to attend conference (at least, online).
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