Research Achievements

Papers:

1. Tame arrangements, T. Abe, arXiv:2504.14902.

2. Solomon-Terao polynomials and Castelnouvo-Mumford regularity of hyperplane arrangements, T. Abe, arXiv:2509.10047

3. Addition theorems for Ziegler pairs of hyperplane arrangements T. Abe, L. Kühne, P. Pokora, arXiv:2509.19011 

4. On Universal derivations for multiarrangements,  T. Abe, S. Maehara, G. Roehrle, S. Wiesner, arXiv:2511.05086

Talks (at international conferences): 

1. Tame arrangements, Takuro Abe, at New perspectives on hyperplane arrangements (RUB, Bochum, Germany), 14 May 2025.

2. Tame arrangements, Takuro Abe, Moduli and Friends II (online, organized by Romanian team), 26 May 2025.

3. Free path and restrictions of hyperplane arrangements, Takuro Abe, Oberseminar Groups and Geometry (Bielefeld University,  Bielefeld, Germany), 1 July 2025.

4. Restriction of free arrangements, Takuro Abe, Topology of Arrangements with an Eye to Applications (University of Pisa), 5 September 2025.

5. Castelouvo-Mumford regularity and Solomon-Terao polynomial of hyperplane arrangements, Takuro Abe, Moduli, Hilbert Schemes and Singularities (Babeș-Bolyai University), 8 September 2025.

6. Regularity of logarithmic modules of hyperplane arrangements, Takuro Abe, at AMS Fall Southeastern Meeting 2025 Special Session on Hyperplane arrangements and Polytopes (Tulane University, New Orleans, USA), 5 October 2025.

Poster Presentations:

1. ψ complete graphical arrangements and MAT-free arrangements, Koki Maeda (Kyushu University), Topology of Arrangements with an Eye to Applications (University of Pisa), 2 September 2025.

Conferences:

1. "Arrangement Days in NITech" (Nagoya Institute of Technology, June 11-12, 2025)

2. International Conference "New perspectives of coinvariant rings from viewpoints of geometry and algebraic combinatorics" (RIMS, Kyoto University, July 14-18, 2025)

3. International Conference "Deepning and Applications of Computational Algebraic Geometry via Gröbner bases" (RIMS, Kyoto University, September 9-12, 2025)

4. International Conference "Workshop on Algebraic Geometry in Kanazawa" (Kanazawa, December 1-5, 2025)

5. International Conference "Arrangements in Osaka 2025" (The University of Osaka, Toyonaka Campus, December 15-19, 2025)

Seminars:

• Applied Mathematics Seminar in Rikkyo University

#1 May 22, 2025, Shizuo Kaji (Kyushu University / Kyoto University)

#2 September 8, 2025, Bruno Buchberger (Johannes Kepler University)

• Hyperplane Arrangements Seminar

Visitors:

1. Xavier Roulleau (University of Angers) May 9, 2025

2. Satoshi Murai (Waseda University) June 3, 2025

3. Yasuhide Numata (Hokkaido University) June 13, 2025

4. Hirotachi Abo (University of Idaho) June 18, 2025

5. Leonie Mühlherr (Bielefeld University) July 9-10, 2025

6. Graham Denham (University of West Ontario) August 4-5, 2025

7. Paul Mücksch (Leibniz University Hannover) December 4-10, 2025