I worked as a researcher for a pure mathematics until September 2015. This page is just a log of my reserch during the period.
I studied differentiable/Deligne–Mumford stacks in symplectic/algebraic geometry and topology. My research projects involve especially
- Geometric combinatorics of symplectic toric Deligne–Mumford stacks, and
- The moduli spaces of symplectic vortices in relation to Gromov–Witten theory.
In relation to these projects, I am interested in the following theories.
- Deligne–Mumford stacks, geometric invariant theory, derived algebraic geometry
- Gromov–Witten theory, symplectic vortex equations, Hamiltonian actions
- differentiable stacks, Lie groupoids/algebroids, equivariant topology, Quantisation
The rest of this page is the list of my works and activities in which I attended.
List of research articles (publications and preprints)
- The lattice points of a stacky polytope. Preprint, arXiv:1408.6683.
- On symplectic vortex equations over a compact orbifold Riemann surface. Journal of Symplectic Geometry, 15(4):1129–1171, 2017. (MPIM Preprint)
- The orbitwise volume form and geometry of a Deligne–Mumford stack. Journal of Geometry, 2015.
- (with M. Guest) Orbifold quantum D-modules associated to weighted projective spaces. Commentarii Mathematici Helvetici 89(2):273–297, 2014.
- The symplectic Deligne–Mumford stack associated to a stacky polytope. Results in Mathematics 63(3-4):903–922, June 2013.
- A construction of a Frobenius manifold from the quantum differential equation of a weighted projective space. In Riemann Surfaces Harmonic Maps and Visualization, volume 3 of OCAMI Studies, pages 137–148. Osaka Municipal Universities Press, 2010.
- Gromov–Witten invariants of Fano hypersurfaces, revisited. Journal of Geometry and Physics 58(5):654–669, 2008.
- Normalization of quantum D-modules (量子D加群の正規化). PhD thesis, Tokyo Metropolitan University, March 2009.
- 超曲面の量子コホモロジー (Quantum cohomology of a hypersurface). Master thesis, Tokyo Metropolitan University, March 2005.
- Apr 2009 Instructor for Complex Analysis at Hosei University, Japan
- Apr 2009 Instructor for Calculus at Hitotsubashi University, Japan
List of Talks at Conferences, Workshops, etc.
- "Prequantisations and stacky polytopes", 22nd NRW Topology Meeting, Universität Bonn, 22 November 2014.
- "Prequantisations and stacky polytopes", Deformation Quantization and Algebraic Index Theorems, University of Copenhagen, October 2014.
- "The symplectic vortex equations and Gromov-Witten invariants" (two lectures), Koriyama Geometry and Physics Days 2014, Nihon University, October 2014.
- "The moduli spaces of symplectic vortices on an orbifold Riemann surface", Higher Structures in Algebraic Analysis, the University of Padua, February 2014.
- "Noneffective symplectic toric orbifolds and labelled polytopes", The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis, National Taiwan University, March 2010.
- "Normalization of differential equations associated to orbifold quantum cohomology", Riemann Surfaces, Harmonic Maps and Visualization, Osaka City University, December 2008.
- "Restoration of quantum orbifold cohomology from quantum D-modules", Geometry Symposium, Hirosaki University, August 2008.
- "Quantum D-modules and the Birkhoff factorization", Workshop on Schubert calculus 2008, Kansai Seminar House, March 2008.
- "Quantum cohomology of weighted projective spaces", Geometry related to Integrable Systems II, Nara International Seminar House, September 2007.
- "The Birkhoff factorization and efficient computation of Gromov-Witten invariants of Fano hypersurfaces", Geometry, Integrable Systems and Visualization, Osaka City University, January 2006.
- "Gromov-Witten invariants of Fano and Calabi-Yau hypersurfaces", Quantum Cohomology and Mirror Symmetry Day, Tokyo Metropolitan University, January 2005.
List of Talks at Seminars
- "Introduction to Gromov–Witten theory", Leray Topology Seminar, the University of Münster, June 2015.
- "Prequantisations and stacky polytopes", Leray Topology Seminar, the University of Münster, November 2014.
- "Combinatorics of symplectic toric Deligne–Mumford stacks", Waseda University, September 2014.
- "Hamiltonian group actions and differentiable stacks (1)–(2)", Leray Topology Seminar, the University of Münster, April 2013.
- "On application of differentiable stacks to symplectic vortex equations", Oberseminar Topologie, the University of Münster, October 2012.
- "On extension of symplectic vortex equation", MPI-Oberseminar, Max Planck Institute for Mathematics, October 2011.
- "Quantum Cohomology and Integrable Systems I–V", Taida Institute of Mathematical Sciences, April–June 2010.
- "Noneffective symplectic toric orbifolds", NCTS (South) Geometry Seminar, National Cheng Kung University, March 2010.
- "Symplectic DM stacks (I)–(III)", NCTS (South) Geometry Seminar, National Cheng Kung University, November–December 2009.
- "Quantum differential equations of weighted projective spaces", NCTS/TPE and TIMS Joint Geometry Seminar, Taida Institute of Mathematical Sciences, October 2009.
- "Normalization of differential equations associated to orbifold quantum cohomology", Algebraic geometry seminar, the next generation, Tokyo Metropolitan University, January 2009.
- "Restoration of quantum orbifold cohomology from quantum D-modules", Keio Geometry Seminar, Keio University, July 2008.
- "Restoration of quantum orbifold cohomology from quantum D-modules", Differential Geometry Seminar, Osaka City University, July 2008.
List of Activities which I attended. (2010–2014)
- 22nd NRW Topology Meeting, Universität Bonn, 21–22 Nov 2014.
- Deformation Quantization and Algebraic Index Theorems, University of Copenhagen, 27–31 Oct 2014.
- Koriyama Geometry and Physics Days 2014, Nihon University, 04–06 Oct 2014.
- Loop spaces in geometry and topology, Université de Nantes, 01–05 Sep 2014.
- Three Conner-Floyd type theorems in the motivic context, Universität Duisburg-Essen, 16–20 Jun 2014.
- Higher Structures in Algebraic Analysis, University of Padova, 10–21 Feb 2014.
- Hamiltonian Systems and Celestial Mechanics, Universität zu Köln, 29 Jul–02 Aug 2013.
- GESTA workshop, Université Paul Sabatier, 03–07 Jun 2013.
- Minicourse "Free loop spaces in topology and physics", Universität Münster, 22–24 Apr 2013.
- Minicourse: Vortices and Quantum Kirwan Maps, HIM, 11–12 Dec 2012.
- Geometric Dynamic Days, Universität Münster, 07–08 Dec 2012.
- Geometry of the Vortex Equations, HIM, 27–30 Nov 2012.
- 18th NRW Topology Meeting, Universität Bielefeld, 16–17 Nov 2012.
- Mathematics and Physics of Moduli Spaces, Universität Heidelberg, 24–28 Sep 2012.
- Poisson 2012, Utrecht University, 23–27 Jul 2012.
- Integrability in topological field theory, HIM, 16–20 Apr 2012.
- Master Class: Vortex equations and Hamiltonian GW invariants, QGM, 17–20 Jan 2012.
- Integrability - modern variations, HIM, 09–13 Jan 2012.
- Higher Structures 2011, Universitiät Göttingen, 28 Nov–02 Dec 2011.
- Finite Dimensional Integrable Systems in Geometry and Mathematical Physics 2011, Universität Jena, 26–27 Jul 2011.
- The Second Taiwan Geometry Symposium, NCTS (Taipei), 14 May 2011.
- The First Taiwan Geometry Symposium, NCTS (South), 20 Nov 2010.
- The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis, NTU, 21–23 Mar 2010.
- Symplectic & Contact Winter School, NCTS (South), 24–27 Feb 2010.
- Journal referee: Geometry & Topology
- Membership: European Mathematical Society (until 2015)
- Membership: German Mathematical Society (Deutsche Mathematiker-Vereinigung) (until 2015)