Shi-shyr Roan received a B.S. and a M.S. from the Mathematical Department of National Taiwan University in 1966 and 1968 respectively. He received a Ph.D. in mathematics from Brandeis University, U.S.A. in 1974. Over the years, Roan taught at various universities: U.C. Berkeley, U.S.A. (1974-1976), National Tsing Hua University, Taiwan (1976-1988), Clark University, U.S.A. (1988-1989). He was a member of Institute for Advanced Study, Princeton, U.S.A. in 1981-1982. As a visiting professor, he conducted researches at Research Institute for Mathematical Sciences, Kyoto University, Japan in 1989-1990, and at Max-Planck-Institut fur Mathematik, Bonn, Germany, in 1990-1993. He jointed the Institute of Mathematics, Academia Sinica on July, 1993.
FIELDS OF RESEARCH
Complex variety with trivial canonical bundle, Orbifold geometry, Toric geometry.
Mathematical Physics : 2-dimensional solvable statistical mechanics, Quantum integrable systems, String theory.
PUBLICATIONS (2004 - )
1. On hypersurface quotient singularity of dimension 4, Intern. J. Math. & Math. Sciences , 48 (2004) 2547-2581; math.AG/0011151, (with L. Chiang).
2. On branching indices of affine A-D-E diagrams : a geometrical characterization by Kleinian singularities, math.AG/0405580.
3. Intermediate Jacobian and some arithmetic properties of Kummer-surface-type CY 3-folds, math.AG/0407193.
4. Bethe Ansatz equations of XXZ model and q-Sturm-Liouville problems, math-ph/0407033 (with Mourad E. H. Ismail and S. S. Lin ).
5. Chiral Potts rapidity curve descended from six-vertex model and symmetry group of rapidities,J. Phys. A: Math. Gen. 38 (2005) 7483-7499; cond-mat/0410011.
6. Structure of certain Chebyshev-type polynomials in Onsager's algebra representation, Journal of Computational and Applied Mathematics 202 (2007) 88-104; math-ph/0501045.
7. The Onsager algebra symmetry of τ(j) -matrices in the superintegrable chiral Potts Model, J. Stat. Mech. (2005) P09007; cond-mat/0505698.
8. Bethe ansatz and symmetry in superintegrable chiral Potts model and root-of-unity six-vertex model, in Nankai Tracts in Mathematics Vol. 10, Differential Geometry and Physics, ed, Mo-Lin Go and Weiping Zhang (World Scientific, Singapore 2006), pp 399-409; cond-mat/0511543 .
9. The Q-operator for root-of-unity symmetry in six vertex model,J. Phys. A: Math. Gen. 39 (2006) 12303-12325 ; cond-mat/0602375.
10. Fusion operators in the generalized τ(2)-model and root-of-unity symmetry of the XXZ spin chain
of higher spin, J. Phys. A: Math. Theor. 40 (2007) 1481-1511; cond-mat/0607258.
11. The Q-operator and functional relations of the eight-vertex model at root-of-unity η = 2mK/N for odd N, J. Phys. A: Math. Theor. 40 (2007) 11019-11044; cond-mat/0611316.
12. On Q-operators of XXZ spin chain of higher spin, cond-mat/ 0702271.
13. The transfer matrix of superintegrable chiral Potts model as the Q-operator of root-of-unity XXZ chain with cyclic representation of Uq(sl2), J. Stat. Mech. (2007) P09021; arXiv: 0705.2856.
14. On the equivalent theory of the generalized τ(2) -model and the chiral Potts model with two alternating vertical rapidities, arXiv: 0710.2764.
15. Bethe equation of τ(2)-model and eigenvalues of finite-size transfer matrix of chiral Potts model with alternating rapidities, J. Stat. Mech. (2008) P10001; arXiv.0805.1585.
16. On τ(2)-model in chiral Potts model and cyclic representation of quantum group Uq(sl2), J. Phys. A: Math. Theor. 42 (2009) 072003; arXiv:0806.0216.
17. Duality and symmetry in chiral Potts model, J. Stat. Mech. (2009) P08012; arXiv:0905.1924.
18. Eigenvectors of an arbitrary Onsager sector in superintegrable τ(2)-model and chiral Potts model, arXiv:1003.3621
19. Toric representation and positive cone of Picard group and deformation space in mirror symmetry of Calabi-Yau hypersurfaces in toric varieties,
21. Fermat surface and group theory in symmetry of rapidity family in chiral Potts model, arXiv:1301.5260
PUBLICATIONS (1994- 2003 )
1. Topological properties of Calabi-Yau manifolds, in: R. Penner and S. T. Yau (Ed.), Perspectives in Mathematical Physics, Intern. Press, 1994, pp. 251-264.
2. On c1 = 0 resolution of quotient singularity, Intern. J. Math. 5 (4) (1994) 523-536.
3. A stochastic approach to Euler Poincare number of loop space of a developable orbifold, J. Geom. Phys. 16 (1995) 71- 98, (with R. Leandre ) .
3. Minimal resolutions of Gorenstein orbifolds in dimension three, Topology 35 (1996) 489-508.
5. A note on ODEs from mirror symmetry, in: Functional analysis on the eve of the 21st century-in honor of the 80th birthday of I.M. Gelfand, Vol. II , Birkhäser Boston, Inc.; 1996, pp. 301- 32 ; hepth/9407192 , ( with A. Klemm, B. H. Lian and S. T. Yau ).
6. Toric geometry in mirror geometry, Academia Sinica Math. preprint R940907-1, 1994.
7. Picard groups of hypersurfaces in toric varieties, Publ. RIMS Kyoto Univ. 32 (1996) 797-834; arXiv:1106.1615
8. Mirror symmetry of elliptic curves and Ising model, J. Geom. Phys. 20 (1996) 273-296; hep-th/9509051.
9. Weighted projective surfaces of splitting-type, MIAS 95-5, 1995, ( with Y. Goto ) .
10. Bethe Ansatz for Heisenberg XXX model, MIAS 95-6 , 1995, cond-mat /9509183 ( with S.S. Lin ).
11. Orbifold Euler characteristic, in: B. Greene and S. T. Yau (Ed.), Mirror Symmetry II, Amer. Math. Soc., Intern. Press, 1997, pp. 129-140 .
12. Yang-Baxter relation for sl(2)-Yangian, MIAS 96-2, 1996, ( with M. L. Ge and S.S. Lin ).
13. Crepant resolution and fibred CY manifolds, MIAS 97-1, 1997.
14. Calabi-Yau fourfolds for M- and F-Theory compactifications, Nucl. Phys.B 518, 3 (1998) 515-574, hep-th/ 9701023, ( with A. Klemm, B. H. Lian and S. T. Yau ).
15. Gauge symmetry and integrable models, MSRI Preprint 1997-88, hep-th/ 9709073, ( with O. K. Pashaev and S. S. Lin ).
16. Schwarz's function and chiral Potts model, Helv. Phys. Acta 71 (1998) 242-261.
17. The algebraic structure of the Onsager algebra, Czech. J. Phys., Vol. 50 No. 1 (2000) 37-44; cond-mat/0002418, (with E. Date) .
18. The structure of quotients of the Onsager algebra by closed ideals, J. Phys. A: Math. Gen. 33 (2000) 3275-3296; math.QA/9911018, (with E. Date) .
19. Heisenberg and modular invariance of N=2 conformal field theory, Intern. J. Mod. Phys. A, 15 (2000) 3065-3094; hep-th/9902198.
20. Algebraic geometry approach to the Bethe equation for Hofstadter type models , J. Phys. A: Math. Gen. 35 (2002) 5907-5933; cond-mat/9912473, (with S. S. Lin) .
21. Orbifolds and finite group representations, Intern. J. Math. & Math. Sciences 26:11 (2001) 649-669, math.AG/0007072, (with L. Chiang).
22. Algebraic geometry and physics, in: T.Sunada, P. W. Sy and Y. Lo (Ed.), Proceedings of the Third Asian Math. Conf. 2000, World Scientific 2002, pp. 455- 482 ; math-ph/0011038.
23. The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials, in: S.Pakuliak and G.von Gehlen (Ed.), Integrable Structure of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, Kluwer Academic Publ., Dordrecht 2001, pp. 155-172; hep-th/0104144, (with G. von Gehlen).
24. Baxter's T-Q relation and Bethe Ansatz of discrete quantum pendulum and sine-Gordon model, hep-th/0105140, ( with S. S. Lin ).
25. Algebraic geometry in discrete quantum integrable model and Baxter's T-Q relation, Czech. J. Phys., 52 (2002) 737-820; hep-th/0107047, (with S. S. Lin ).
26. Characters of representations of affine sl(2|1) algebra and N=2 superconformal algebra, preprint, 2002, (with V. Kac and M. Wakimoto).
27. Algebraic geometry and Hofstadter model, Intern. J. Mod. Phys. B, 16 (2002) 2097- 2106; math-ph/0206014, (with S. S. Lin ).
28. Crepant resolutions of C^n/A_1(n) and flops of n-folds for n= 4, 5 , in: N. Yui and J. D. Lewis (Ed.), Calabi-Yau varieties and mirror symmetry, Fields Institute Comm. 38 , 2003, Amer. Math. Soc. Pp. 27-41 ; math.AG/0208052, (with L. Chiang).
29. Quantum reduction for affine superalgebras, Comm. Math. Phys. 241 (2003) 307-342; math-ph/0302015, (with V. Kac and M. Wakimoto).
30. Rational curves in rigid Calabi-Yau three-folds, math.AG/0312399.
PUBLICATIONS (1984- 1993 )
1. Homogeneous vector bundles over projective varieties, Chinese J. Math. 12 (1984) 137-169.
2. On Ricci flat 3-fold , Acta Mathematica Sinica, New Series, Beijing 3 (3) (1987) 256-288, ( with S. T. Yau ).
3. On the generalization of Kummer surfaces, J. Diff. Geom. 30 (1989) 523 - 537.
4. On the Calabi-Yau orbifolds in weighted projective spaces, Intern. J. Math. 1 (2) (1990) 211-232.
5. Excitation spectrum and phase structure of chiral Potts model, Phys. Lett. A 150 (1990) 347-354, (with B. M. McCoy ).
6. Geometric singularities and spectra of Landau-Ginzburg models, Comm. Math. Phys. 142 (1991) 245-259, ( with B. R. Greene and S. T. Yau ).
7. The mirror of Calabi-Yau orbifold, Intern. J. Math. 2 (4) (1991) 439-455.
8. A characterization of "rapidity" curve in chiral Potts model, Comm. Math. Phys. 145 (1992) 605-634.
9. Modular invariance of manifolds with SU(n) holonomy, Intern. J. Math. 3 (3) (1992) 359-395.
10. Vafa's formula and equivariant K-theory, J. Geom. Phys. 10 (1993) 287-294, (with K. Ono ).
11. Onsager's algebra, loop algebra and chiral Potts model, Preprint Max-Planck-Inst. Fur Math., Bonn, MPI 91-70, 1991.
12. Abelian integral in chiral Potts model, Preprint Max-Planck-Inst. fur Math., Bonn, MPI 92-27, 1992.
13. Mirror symmetry and Arnold's duality, Preprint Max-Planck-Inst. fur Math., Bonn, MPI 92-86,1992; Zap. Nauchn. Sem. POMI 234 (1996) 153-176, (English): J. Math. Sci. (New York), 94 (1999), 1237-1253.
14. The geometry of Calabi-Yau orbifolds, in: S.T Yau (Ed.), Essays on mirror manifolds, Intern. Press, Hong Kong, 1992, pp. 342-348.
15. New constructions of mirror manifolds: probing moduli space far from Fermat points. In: S.T Yau (Ed.), Essays on mirror manifolds, Intern. Press, Hong Kong, 1992, pp. 408-448 (with B. R. Greene and M. R. L. Plesser).
16. Topological coupling of Calabi-Yau orbifold, J. Group Theory in Physics 1 (1993) 83- 103.
17. A new example of N=2 supersymmetric Laudau-Ginzburg theories: the two ring case, Mod. Phys. Lett. A 8 (31) (1993) 2989-2999; math-ph/0209061 ( with A. M. Perelomov ).
PUBLICATIONS (1974- 1983 )
1. Degeneration of K3 and abelian surfaces, Ph.D. thesis of Brandeis University , 1974.
2. A remark on Grauert's theorem, Bull. Inst. Math. Academia Sinica 5 (1977) 167-170.
3. Subvarieties of codimension ≧ 2, Bull. Inst. Math. Academia Sinica 6 (1978) 189-196.
5. The configuration of singular varieties, Bull. Inst. Math. Academia Sinica 7 (1979) 419-429.
5. The fundamental group of residual space of a curve in an algebraic surface, Chinese J. Math. 7 (1979) 163-175.
6. Branched covering spaces, Chinese J. Math. 7 (1979) 177-206.
7. Picard-Lefschetz transformation on homotopy group, Chinese J. Math. 9 (1981) 81-90.
8. Subbundles of the tangent bundle of the complex projective spaces, Bull. Inst. Math. Academia Sinica 9 (1981) 1-28.
9. On elliptic fiber surfaces, Chinese J. Math. 11 (1983) 129-142.
10. On flat fiber surfaces, Chinese J. Math. 11 (1983) 157-180.