Combinatorics of hyperplane arrangements and symplectic algebraic geometry from multiple point of view
Takahiro Nagaoka
Doctoral Student, Graduate School of Science, Department of Mathematics
Host Institution: Max Planck Institute for Mathematics in the Sciences (Leipzig)
Duration of stay: January 16 - February 1, 2019

Host Institution:

  • Prof. Mateusz Michalek, Max Planck Institute for Mathematics in the Sciences (Leipzig)

Visited Researchers and Institutions: 

  • Prof. Gwyn Bellamy, University of Glasgow

Duration of stay:

  • September 14 to September 30, 2018


  • Building a new research networks at research institutes in Germany
  • Presentation and discussion of research at different universities

Participated events 

  • Geometry and Topology Seminar, University of Glasgow, September 17, 2018)
  • Seminar on Nonlinear Algebra, Max-Planck Institutes, Leipzig, September 26, 2018

Motivation for AIDA application

During my master course, I studied hypertoric variety, which is a special class of symplectic varieties. In my thesis, I proved its properties by using combinatorics of hyperplane arrangements. I have two reasons why I applied for the AIDA program. First, Germany, in particular Max Planck Institute, is a worldwide-acknowledged leader in research on algebraic geometry from the perspectives of combinatorics. Therefore, I thought staying at MPI could advance my research by receiving feedback from fellow researchers and by building networks that would lead to collaborations in the future.

My second reason was an invitation by Prof. Misha Feigin, who gave a talk at Kyoto University in June 2018. He offered me a chance to present my work at Glasgow University, if I ever came to Europe. I also hoped to discuss my research with him and his colleague Prof. Gwyn Bellamy, both experts in my research area, in order to improve my research.



Networking with researchers from Max Planck Institute (MPI)

During my 2 weeks stay at MPI, Prof. Mateusz Michalek introduced me to the members of his research group. We discussed each other’s research projects, sharing advice and opinions. On the weekends, we went hiking together which fostered a good relationship with the team members.

Giving a presentation in the Nonlinear Algebra Seminar at MPI

Aside from the rather informal explanation of my research topic to the research group members, I also gave a presentation at the (formal) weekly Nonlinear Algebra Seminar. The audience seemed to be very interested in my research and I received a lot feedback and interesting questions.

Giving a presentation in the Geometry Seminar at Glasgow University

I gave a one-hour long presentation at Glasgow University in front of experts in my research field. Beyond that Prof. Gwyn Bellamy arranged a meeting and took some time to discuss my work with me. Through this, I was able to get many precious comments that will surely improve my future research.


By visiting Germany as well as Scotland, I realized the importance of meeting and networking with researchers in person. It also encouraged me to expand my network with researchers across European in future.

Equally important, my research during PhD course will greatly benefit thanks to the comments provided by Prof. G. Bellamy on my M.S. thesis and the ongoing exchange with him.