River Chiang (NCKU)

2009/06/22-Present, Coordinator of Division of Mathematics, NCTS(South)

Symplectic geometry, Topology

Tel: +886-6-2757575 Ext. 65126


Introduction :

Geometry has many interesting different aspects, and our focus group has a wide spectrum which covers quite a few important directions of them. We mostly concentrate on, but not limited to: Geometric Evolution Equations, Function and Map Theory, and Geometric Structures. During the year, we have many regular seminars and held quite a few conferences and mini courses.


Main research focus of GADG group at NCTS:

• Geometric Evolution Equations:

(i) Mean curvature flow in higher co-dimension

(ii) The torsion flow and geometrization problem of contact 3-manifolds

(iii) The curvature flow of curves and hypersurfaces

(a) Expanding convex immersed closed plane curves

(b) Evolving a convex closed curve to another one via a length-preserving linear flow

(c) Contracting convex immersed closed plane curves


• Function and Map Theory :

(i) Function theory on pseudohermitian manifolds.

(ii) Analysis on sub-manifold in a sub-Riemannian manifold

(iii) Harmonic function Theory

(a) Minimal submanifolds

(b) Harmonic functions and harmonic forms on manifolds

(c) Heat flow of Harmonic Maps Heat flow of Harmonic Maps


• Geometric Structures :

(i) Special Lagrangian and Hamiltonian stationary sub-manifolds

(ii) CR structures in Cauchy-Riemann geometry and topology of contact manifolds

(iii) The Calabi-Yau problems for CR manifolds.


Other Topics :

The geometry research at Tainan ranges from symplectic geometry to algebraic geometry to geometric analysis. Research topics include: moduli spaces of vector bundles, representation varieties, moment maps in various geometries, contact homology, Lagrangian submanifolds, orbifold quantum cohomology, cohomological crepant resolutions, local positivity and syzygies of algebraic varieties, geometric flows and harmonic maps.