Algebraic Structure with Applications to Mathematical Physics


Ching Hung Lam (NCKU)

Vertex Algebras, Lie Algebras, Finite Group Theory

Tel: +886-6-2757575 Ext. 65142



The main theme for the algebra group is on the structure and representation theory of quantum algebras and their related topics. The topics include:

  1. the representation theory of infinite dimensional Lie algebras, super-algebras and vertex algebras and the determination of their characters, fusion rules and modular invariants.
  2. the representation theory of classical groups and algebraic groups.
  3. the applications of representation theory to conformal field theory, number theory, finite group theory and algebraic geometry;
  4. related combinatorial structures and their applications such as design theory, error correcting codes and quantum error correcting codes.



Interactions between Differential Geometry, Partial Differential Equations, and Algebraic Geometry


Eugene Xia (NCKU)

Algebraic Geometry

Tel: +886-6-2757575 Ext. 65159



The geometry group at NCTS South have specialists in global analysis, symplectic and algebraic geometry. More specifically:

  1. Global Analysis and Algebraic geometry: The solvability of various partial differential equations on manifolds, including Monge-Ampere Equations (Kaehler-Einstein Equations), Yang-Mills Equations, Einstein-Hermitian Equations on manifolds, Constant Scalar Curvature equations on Kaehler manifolds; the relations between the solvability of these equations and the various stability conditions in GIT (Geometric Invariant Theory). Geometric Evolution Equations.
  2. Spectral geometry and eigen-value problems.
  3. Moduli Spaces: Higgs bundles on Riemann surfaces, Non-abelian Hodge theory. The representation varieties of the fundamental groups of Riemann surfaces. Ergodic theory and topological dynamics of the mapping class group action on representation varieties.
  4. Moduli of representation varieties of non-orientable surfaces, their volumes and cohomologies.
  5. Symplectic geometry: Symplectic Hodge theory, existence of exotic Lagrangian submanifolds, Symplect Reduction and related classification problems.


Wen Fong Ke (National Cheng Kung University)

Ngau Lam (National Cheng Kung University)

Ching Hung Lam (National Cheng Kung University)

Yung Yu (National Cheng Kung University)

Chufeng Nien (National Cheng Kung University)

Po-Yi Huang (National Cheng Kung University)

Roger Chen (National Cheng-Kung University)

River Chiang (National Cheng-Kung University)

Yungyen Chiang (National Sun-Yat-Sen University)

Sun-Chin Chu (National Chung-Cheng University)

Wen Fong Ke (National Cheng-Kung University)

Nan-Kuo Ho (National Cheng-Kung University)

Ying-Ji Hong (National Cheng-Kung University)

Ching Hung Lam (Chief Coordinator, National Cheng-Kung University)

Ngau Lam (National Cheng-Kung University)

Eugene Xia (National Cheng-Kung University)