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Retired Research Fellows

Roan, Shi-Shyr

Retired Research Fellow

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.

　　Roan's research areas are algebraic geometry, complex geometry, mathematical physics and representation theory. In recent years, he have been working on the geometrical problems related to theoretical physics.

Research Fields: Algebraic Geometry, Complex Geometry, Mathematical Physics

Email : maroan@gate.sinica.edu.tw

Extension : 400

  • "Degeneration of K3 and abelian surfaces, Ph.D. thesis of Brandeis Uniuersity, 1974. "
  • "A remark on Grauert's theorm, Bull. Inst. Math. Academia Sinica, 5(1977), 167-170. "
  • "Subvarieties of condimension 2, Bull. Inst. Math. Academia Sinica, 6(1978), 189-196. "
  • "The configuration of singular varieties, Bull. Inst. Math. Academia Sinica, 7(1979), 419-429. "
  • "The fundamental group of residual space of a curve in an algebraic surface, Chinese J. Math., 7(1979), 163-175. "
  • "Branched covering spaces Chinese J. Math., 7(1979), 177-206. "
  • "Picard-Lefschetz transformation on homotopy group, Chinese J. Math. 9(1981), 81-90. "
  • "Subbundlies of the tangent bundle of the complex projective spaces, Bull. Inst. Math. Academia Sinica 9(1981), 1-28. "
  • "On elliptic fiber surfaces, Chinese J. Math. 11(1983), 129-142. "
  • "On flat fiber surfaces, Chinese J. Math. 11(1983), 157-180. "
  • "A note on cancellation, Chinese J. Math. 11(1983), 319-325. "
  • "Homogeneous vector bundles over projective varieties, Chinese J. Math. 12(1984), 137-169. "
  • "(With Shing-tung Yau) On Ricci flat 3-fold, Acta Mathematica Sinica, New Series, Beijing, 3(3)(1987), 256-288. "
  • "On the generalization of Kummer surfaces, J. Diff. Geom., 30(2), (1989), 523-537. "
  • "On the Calabi-Yau orbifolds in weighted projective spaces, Internat. J. Math., 1(2), (1990), 211-232. "
  • "(With B. M. McCoy) Excitation spectrum and phase structure of chiral Potts model, Phys. Lett. A, 150 (1990), 347-354. "
  • "(With B. R. Greene and S. T. Yan) Geometric singularities and spectra of Landau-Ginzburg models, Comm. Math. Phys., 142(1991), 245-259. "
  • "The mirror of Calabi-Yau orbifold, Internat. J. Math., 2(4), (1991), 439-455. "
  • "A characterization of "rapidity" curve in chiral Potts model, Comm. Math. Phys., 145(1992), 605-634. "
  • "Modular invariance of manifold with SU(n) holonomy, Internat. J. Math., 3(3), (1992), 359-395. "
  • "(With K. Ono) Vafa's formula and equivariant K-theory, J. Geom. Phys., 10(1993), 287-294. "
  • "Onsager's algebra, loop algebra and chiral Potts model, MPI 91-70. "
  • "Abelian integral in chrial Potts model, MPI 92-27. "
  • "Mirror symmetry and arnold's duality, MPI 92-86. "
  • "The geometry of Calabi-Yau orbifolds, Essays on mirror manifolds, Internat. Press, Hong Kong, 1992, 342-348. "
  • "(With B.R. Greene and M.R.L. Plesser) New construction of mirror manifolds: probing moduli space far from Fermat points. Essays on mirror manifolds, Internat. Press Hong Kong, 1992, 408-448. "
  • "Topological coupling of Calabi-Yau orbifold, J. Group Theory in Physics, 1(1993), 83-103. "
  • "(With A.M. Perelomov) A new example of N=2 supersymmetric Laudau-Ginzburg theories: the two ring case, Modern Phys. Lett. A8(31), (1993), 2989-2999. "
  • "Topological properties of Calabi-Yau manifolds, in Perspectives in mathematical Physics(edited by B. R. Greene and S. T. Yau) International Press, (1994), 251-264. "
  • "On = 0 resolution of quotient singularity, Internat. J. Math., 5(4)(1994), 523-536. "
  • "(With R. Leandre) A stochastic approach to Euler Poincare number of loop space of adevelopable orbifold, J. Geom. Phys., 16(1995), 71-98. "
  • "Minimal resolutions of Gorenstein orbifolds in dimension three, Topology, 35(1996), 489-508. "
  • "(With A. Klemm, B. H. Lian and S. T. Yau) A note on ODEs from mirror symmetry, Functional analysis on the eve of the 21st century-in honor of the 80 birthday of I.M. Gelfand, vol. 11,301-323, (1996) Birkhaser Boston, Inc. "
  • "Toric geometry in mirror geometry, Academia Sinica Math. preprint R940907-1. "
  • "Picard groups of hypersufaces in toric varieties, Publ. RIMS, Kyoto Univ., 32(1996), 797-834. "
  • "Mirror symmetry of elliptic curves and Ising model, J. Geom. Phys., 20(1996), 273-296. "
  • "(With Y. Goto) Weighted projective sufaces of splitting-type, MIAS 95-5. "
  • "(With S. S. Lin) Bethe Ansatz for Heisenberg XXX model, MIAS 95-6, cond-mat/9509183. "
  • "Resolutions of quotient singularities, Proc. Natl. Sci. Counc., ROC(A), 20(6) (1996), 593-598. "
  • "Orbifold Euler characteristic, in Mirror Symmetry II, 129-140 (edited by B. Greene and S. T. Yau) American Mathematical Society, International Press, 1997. "
  • "(With M. L. Ge and S. S. Lin) Yang-baxter relation for sl(2)-Yangian, MIAS 96-2. "
  • "Crepant resolution and fibred CY manifold, MIAS 97-1. "
  • "(With A. Klemm, B. H. Lian and S. T. Yau) Calabi-Yau fourfolds for M-and F-Theory compactifications, Nucl. Phys. B5183 (1998), 515-574, hep-th/9701023. "
  • "(With O. K. Pashaev and S. S. Lin) Gauge symmetry and integrable models, MSRI Preprint 1977-88, hep-th/9709073. "
  • "Schwarz's fuction and chiral Potts model, Helvetical Acta, 71(1998), 242-261. "
  • "Heisenberg and modular invariance of N = 2 conformal field theory, (to appear in Intern. J. Mod. Phys. A), MIAS 99-1, hep-th/9902198. "
  • "(With E. Date) The algebraic structure of the Onsager algebra, Czechoslovak Journal of Physics, 50(1), (2000), 37-44, cond-mat/002418. "
  • "(With E. Date) The structure of quotients of the Onsager algebra by closed ideals, (to appear in Phys. A), math-QA/9911018. "
  • "(With S. S. Lin) Algebraic geometry approach to the Bethe equation for Hofstadter type models, cond-mat/9912473. "
  • "The Q-operator for root-of-unity symmetry in six vertex model", Journal of Physics A: Mathemtical and Geneneral, 39 (40), 12303-12325, 2006
  • "Structure of certain Chebyshev-type polynomials in Onsager’s algebra representation,", Journal of Computational and Applied Mathematics(math-ph/0501045.), 2006-04
  • "Bethe ansatz and symmetry in superintegrable chiral Potts model and root-of-unity six-vertex model", Differential Methods in Theoretical Physics(E-arXiv: cond-mat/0511543.), 2005-11
  • "Fusion operators in the generalizedτ(2) -model and the root-of-unity symmetry of six-vertex model with a higher spin,", E-arXiv: cond-mat/0607258.
  • "The Q-operator and functional relations of the eight-vertex model at root-of-unity η = 2mK/N for odd N", E-arXiv: cond-mat/ 0611316.
  • "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
  • "On the equivalent theory of the generalized $\tau^{(2)}$model and the chiral Potts model with two alternating vertical rapidities", 2008
  • "Bethe equation of $\tau^{(2)}$-model and eigenvalues of finite-size transfer matrix of chiral Potts model with alternating rapidities", 2008
  • "On $\tau^{(2)}$-model in chiral Potts model and cyclic representation of quantum groupUq(sl2)", 2008
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