WeiHung Liao

Bio

Weihong Liao is currently a postdoctoral researcher at the Shanghai Institute for Mathematics and Interdisciplinary Research. He got his Ph.D at National Taiwan University and he focused on the theoretical analysis of curvature flow to reduce the energy functional of surfaces to reach the standard fundamental surfaces.

Future research interests are divided into three directions: 1. Consider the dual discrete Laplacian and utilize the geometric properties of the mean curvature of the continuous Laplacian on hypersurfaces to give geometric curvature reflecting geometric curvature closer to that in continuum theory. 2. Consider angle-preserving and area-preserving problems for surfaces of genus-1, taking into account from a two-dimensional complex space. 3. The geometry of the 2-dimensional complex space is used to find out the energy functionals to compute the optimization of the conformal or area preserving properties, which is an attempt to push forward the theory of interactive superposition optimization and R-linear convergence in the previous paper, and also to give a different computational method from the one proposed in the earlier study, which is based on the use of holomorphic differentials to compute the conformal mapping. 3. The problem is related to that of the decomposition of a high-genus surface into a number of partially standardized tires to generate the conformal and area-preserving problems of a higher genus surface. This problem is closely related to the decomposition of a higher genus surface into several standard tire surfaces and the problem of area preservation, as well as to the distribution of singularities in the initial triangular mesh to generate the quadrilateral mesh.

Education Experience

• 2012-2019 National Taiwan University Mathematics Doctor

Work Experience

• 2020-2024 National Yang Ming Chiao Tung University Postdoc
• 2024- Shanghai Institute for Mathematics and Interdisciplinary Sciences Postdoc

Publication

More details in CV