2020 Fiscal Year Research-status Report
On the algebra and combinatorics of hyperplane arrangements
Project/Area Number |
19K14493
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Research Institution | Hokkaido University |
Principal Investigator |
トリエッリ ミケーレ 北海道大学, 理学研究院, 助教 (10780124)
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Project Period (FY) |
2019-04-01 – 2022-03-31
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Keywords | Hyperplane arrangements / Lefschetz properties / Domination theory / Gain graphs |
Outline of Annual Research Achievements |
During the last academic year, I continued my studies on algebraic and combinatorial invariants of hyperplane arrangements, with special emphasis to the class of free hyperplane arrangements and Terao's conjecture. In addition, I extended these studies to the class of multiarrangements, to the class of plus-one generated arrangements and to analyze the connection between freeness and Lefschetz properties. In addition, I continued my work on domination theory for graphs, In doing so, I got 6 papers accepted for publication in peer reviewed journals, and submitted 3 new papers for publication. These new papers are all natural extensions of my previous papers. In fact, the ideas developed in them are the results of questions and suggestions I received during my oral presentations at conferences. In the same period, I also took part in 5 international online workshops. Moreover, I was invited to give oral presentations in two conference that were all postponed by Covid-19.
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Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
As mentioned above, during the past academic year I manage to have a constant research output, submitting 3 new papers for publication and taking part in 5 international online workshops. In addition, the work I have done fits perfectly wth my research goals and it will be fundamental in the next few years in order to be able to continue my research output.
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Strategy for Future Research Activity |
I plan to continue my research on algebraic and combinatorial invariants of hyperplane arrangements, with special emphasis to the class of free hyperplane arrangements in order to get closer to solve Terao's conjecture. Specifically, I plan to study in depth the class of real complexified arrangements, using the techniques developed in my recent papers on modular methods for freeness and combinatorial invariants, and on the Lefschetz properties of Jacobian algebras. In addition, I plan to take part regularly to meeting and workshops, in order to expand my list of collaborators even further and to make my research known to all researchers in my field.
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Causes of Carryover |
Next academic year, I plan to attend several conferences and international meetings (COVID permitting). Moreover, I would like to buy several mathematical books.
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Research Products
(7 results)