| Toshio Sumi | Last modified date：2013.5.22 |
Graduate School
Homepage
[URL].
Academic Degree
Dr. Sci.
Field of Specialization
Topology
Outline Activities
My research focuses on transformation theories. I am currently interested in the interactions between finite group actions on spheres and representations of finite groups.
Also I am studying the rank of tensors which are applied in various fields.
I has contributed to the education focusing on mathematical approaches to developing media environments in highly advanced information societies.
Also I am studying the rank of tensors which are applied in various fields.
I has contributed to the education focusing on mathematical approaches to developing media environments in highly advanced information societies.
Research
Research Interests
- Rank, Typical rank of higher order tensors
keyword : tensor, arrays, rank, typical rank, generic rank
2008.07. - Finite group action on a sphere with two fixed points and tangential representation spaces
keyword : group action, sphere, tangential representation
2006.08.
Reports
| 1. | 角 俊雄,Finite groups with Smith equivalent, nonisomorphic representations,変換群論シンポジューム2006報告集,2006.11. |
Papers
| 1. | Krzysztof Pawalowski, Toshio Sumi,The Laitinen Conjecture for finite non-solvable groups,Vol.56,No.1,pp.303-336,2013.02. |
| 2. | Toshio Sumi,Typical ranks for m x n x (m-1)n tensors with m<=n,Linear Algebra and its Applications,Vol.438,No.2,2013.01. |
| 3. | Toshio Sumi,The gap hypothesis for finite groups which have an abelian quotient group not of order a power of 2,Journal of the Mathematical Society of Japan,Vol.64,No.1,pp.91-106,2012.01. |
| 4. | Toshio Sumi and Toshio Sakata,Connectivity for 3x3xK contingency tables,Journal of Algebraic Statistics,Vol.2,No.1,pp.54-74,2011.08 [URL]. |
| 5. | Toshio Sumi and Toshio Sakata,2-neighborhood theorem for 3x3x3 contingency tables,Journal of the Indian Society for Probability and Statistics,Vol.12,pp.66-84,2010.12. |
| 6. | Toshio Sumi and Toshio Sakata,The Set of 3x4x4 Contingency Tables has 3-Neighborhood Property,Proceedings of COMPSTAT'2010, Electronic Supplementary Material (e-book) 19th International Conference on Computational Statistics, Paris France, August 22-27, 2010,pp.1629-1636,2010.09. |
| 7. | Toshio Sumi, Mitsuhiro Miyazaki, and Toshio Sakata,About the maximal rank of 3-tensors over the real and the complex number field,Ann. Inst. Stat. Math.,Vol.62,pp.807-822,2010.09. |
| 8. | Toshio Sumi, Mitsuhiro Miyazaki, and Toshio Sakata,Rank of 3-tensors with 2 slices and Kronecker canonical forms,Linear Algebra and its Applications,vol. 431, 1858-1868,2009.10. |
| 9. | Krzysztof Pawalowski and Toshio Sumi,The Laitinen Conjecture for finite solvable Oliver groups,Proceedings of American Mathematical Society,Proceedings of the American Mathematical Society 137 (6), 2147-2156, 2009,2009.06. |
Presentations
| 1. | The Smith equivalence problem and Smith sets of Oliver groups. |
| 2. | The Smith equivalence problems for finite Oliver groups [URL]. |
| 3. | Nonsolvable groups of which the Smith sets are groups. |
| 4. | Existence and construction of absolutely nonsingular tensors. |
Educational
Educational Activities
My Education activities includes the following lectures
Linear Algebra for first year undergraduated students, discreate mathematics and programming for computer science for third year undergraduated students, and supervising 4th-year undergraduate students and graduate students in master/doctral courses.
Linear Algebra for first year undergraduated students, discreate mathematics and programming for computer science for third year undergraduated students, and supervising 4th-year undergraduate students and graduate students in master/doctral courses.
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