• My Research Story (Japanese)


• Research Interests
• Algebraic geometry (2007 -- current)
birational geometry, vector bundles, pathologies in positive characteristics, singularity theory etc.
• Commutative ring theory (1996 -- current)
Stanley-Reisner rings, affine semi-group rings, projective resolution, local cohomology, monomial ideals, (generalized) Cohen-Macaulay rings, tight closure etc.
• Theoretical computer science (1985 -- 1996)
type theory, constructive logic, program verification and synthesis, concurrency theory, programming environment, etc.
 
• Refereed Papers ( Papers in MathSciNet , Papers in DBLP )
• Theoretical computer science
1. Writing Program as QJ-Proofs and Compiling into PROLOG Programs, 1987 Symposium on Logic Programming, IEEE, pp278-287, 1987
2. QPC: QP-based Proof Compiler -- symple examples and analysis --, 2nd European Symposium on Programming, LNCS 300, Springer, pp49-63, 1988
3. Exteded Projection -- A new method to extract efficient programs from constructive proofs, Functional Programming and Computer Archtecture'89, pp299-312, ACM, 1989
4. Higher Order Programming in QPC^2 , France-Japan Artificial Intelligence and Computer Science Symposium'89, pp299-312, ICOT & INRIA, 1989
5. Extended Projection Method for Proof Compiler (in Japanese), Computer Software, Vol.7 No.4, pp19-38, 1990
6. Extraction of Redundancy-free Programs from Constructive Natural Deduction Proofs, Journal of Symbolic Computation, Vol.12, pp29-69, 1991
7. SHUTEN: A Constructive Programming System (in Japanese) , Journal of Japanese Society for Artificial Intelligence, Vol.7 No.4, 1992
8. Defining Concurrent Processes Constructively , Proceeding of International Conference on Fifth Generation Computer Systems 1992, Vol.2, pp658-665, 1992
9. QPC$_2$: A Constructive Calculus with Parameterized Specifications , Journal of Symbolic Computation, Vol.15, pp641-672, 1993
10. Defining Concurrent Processes Constructively , Theoretical Computer Science, Vol. 122, pp. 137-164, Elisvier, 1994
11. (with S. Hayashi) Lifschitz's Logic of Calculable Numbers and Optimizations in Program Extraction , In Logic, Language and Computation: Festschrift in Honor of Satoru Takasu, Neil D. Jones, Masami Hagiya, Masahiko Sato (Eds.), LNCS No. 792, pp.1-9, Springer-Verlag, 1994
12. Parallelization of Concurrent Processes in Higher Dimensional Automata , RIMS Workshop on Term Rewriting Systems and its Applications, RIMS Kyoto University, 1995
13. Extraction of Concurrent Processes from Higher Dimensional Automata , CAAP'96 (Colloquium on Trees in Algebra and Programming), LNCS 1059, 1996
14. Towards Cycle Filling as Parallelization , RIMS Workshop on Concurrency Theory and Applications '96, RIMS Kyoto University, 1998
• Mathematics
1. (with T. Hibi) Steinit'z theorem analogue for two-dimensional Cohen-Macaulay complexes, Advances in Applied Mathematics Volume 22, Number 2, pp200-218, 1999
2. Normality of Affine Semigroup Rings Generated by 2-dimensional Cone Type Simplicial Complexes,
Communications in Algebra, Vol. 29, No. 4, pp1499-1512, 2001
3. (with J. Herzog) Resolutions by mapping cones, Homology, Homotopy and Applications, vol.4 (2), pp.277-294, 2002.
4. (with J. Herzog) Approximation of generalized Cohen-Macaulay modules, Illinois Journal of Mathematics, vol. 47(4), pp.1287-1302, 2003.
5. Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals, Bull. Math. Soc. Sci. Math. Roumanie, 48(96), no. 3, pp.323--344, 2005
6. (with J. Herzog and N. Terai) On the radical of a monomial ideal, Archiv für Mathematik, Vol.85(5), pp. 397--408, 2005.
7. (with M. Okudaira) Monomial ideals with linear quotients whose Taylor resolutions are minimal, Bull. Math. Soc. Sci. Math. Roumanie, 50(98), no. 2, pp. 161 -- 167, 2007
8. (with S. Goto) Stanley-Reisner ideals whose powers have finite length cohomologies, Proc. Amer. Math. Soc. 135. No.8, pp. 2355--2364, 2007
9. (with J. Herzog, T. Hibi and S. Murai) Componentwise linear ideals with minimal or maximal Betti numbers Ark. Mat. 46 (2008), 69--75
10. (with M. Okudaira) Generalized Complete Intersections with Linear Resolutions Arch. Math. (Basel) 90 (2008), no. 5, 385--394.
11. On non-vanishing of cohomologies of generalized Raynaud polarized surfaces, J. Pure and Applied algebra 214 (2010), no. 7, 1110-1120
12. Raynaud-Mukai construction and Calabi-Yau threefolds in positive characteristic, Proc. Amer. Math. Soc. 140 (2012) no.12, 4063--4074.
13. Kodaira type vanishing theorem for the Hirokado variety, Communications in Algebra 42 (2014). no. 11, 4744--4750
14. Kodaira type vanishing theorem for Calabi-Yau threefolds in positive characteristic, Beitraege zur Algebra und Geometrie, Vol.58 (2017) no.1. 1--11