# Research in NCTU-AM

### Quick Links

### Brief Introduction

The department currently has five research groups: "Mathematical Modeling and Scientific Computing", "Dynamical Systems and Differential Equations", "Discrete Mathematics and Optimization", "Financial Engineering and Probability" and "Number Theory, Geometry and Analysis". Their research includes pattern formations, neural networks, mathematical biology, and chaotic dynamics in Dynamical Systems; nonlinear partial differential equations, fluid mechanics, quantum mechanics, classical mechanics in Differential Equations; numerical PDEs, computational fluid mechanics, interface problems, porous media, and fractured media problems in Scientific Computations; combinatorial optimization, communication networks, algorithms, graph theory, algebraic combinatorics, finite geometry, and combinatorial designs in Discrete Mathematics; contingent claims pricing, credit risk modeling, randomized algorithms and Markov chains in Probability/ Financial Mathematics. The expertise of other faculty include functional analysis, number theory, geometry, and mathematical physics.

These research areas are also well presented at the National Center of Theoretical Sciences (NCTS) hosted by Chiao Tung University and Tsing Hua University. The department faculty members are actively involved in research activities including regular seminars, short courses, workshops, conferences, and summer programs at the NCTS. The faculty members include one national chair professor, two university chair professors, and four professors who were awarded the National Science Council (NSC) distinguished researchership. Almost every faculty member is supported by NSC research project grants.

Main Research Groups (*click header for more information*)

- Mathematical Modeling and Scientific Computing

- Members:

Wen-Wei Lin, Ming-Chih Lai, Chih-Wen Shih, Juang Jonq, Li-Ming Yeh, Chin-Tien Wu, Shu-Ming Chang, Ming-Cheng Shiue, Chi-Hin Chan , Daniel E. Spector , Te-Sheng Lin , Chi-Jer Yu . - Topics:

Large-Scale Matrix Computations, Numerical PDES, Computational Fluid Mechanics, Interface Problems, Porous Media, Fractured Media Problems, Computational Conformal Geometry. - Recent Research Projects:

- Discrete Green function and hybrid deformable models with applications on MRI images registration--Chin-Tien Wu (NSC 104-2115-M-009-002-)
- 3D image registration with applications by using LDDMM--Chin-Tien Wu (NSC 105-2115-M-009-006-)
- Computational Conformal Geometry and Its Applications(4/4)--Wen-Wei Lin (NSC 105-2628-M-009-001-)
- Analysis and Computation in Coupled Phase Equations -- Chih-Wen Shih (NSC 105-2115-M-009-005-MY2)
- Analysis and computation of the related mathematical problems in the atmospheric and oceanic dynamics--Ming-Cheng Shiue (NSC 104-2115-M-009-012-MY2)
- Elliptic equations in random media -- Li-Ming Yeh (NSC 104-2115-M-009-010-MY2)
- Modeling thin nematic films: Weak anchoring model--Te-Sheng Lin (NSC 105-2115-M-009-008-MY2)
- The study of the presence of vortex structures in Navier-Stokes flows passing an abstacle -- Chan Chi Hin (NSC 105-2115-M-009-011-MY2)

Top
- Members:
- Financial Engineering and Probability

- Members:

Yuan-Chung Sheu, Michael Fuchs, Guan-Yu Chen, Yuh-Jye Lee. - Topics:

Probability Theory and Its Applications, Contingent Claims Pricing, Credit Risk Modeling, Randomized Algorithms, Markov Chains. - Recent Research Projects:

- The convergence and dissipation of random walks on specific media--Guan-Yu Chen (NSC 104-2115-M-009-013-MY3)
- Some problems on stochastic portfolio theory--Yuan-Chung Sheu (NSC 105-2115-M-009-009-)

Top
- Members:
- Differential Equations and Dyanmical Systems

- Members:

Song-Sun Lin, Wen-Wei Lin, Chin-Wen Shin, Ming-Chia Li, Juang Jouq, Jong-Eao Lee, Shu-Ming Chang, Chi-Jer Yu, Chi-Hin Chan , Daniel E. Spector . - Topics:

Pattern Formations, Neural Networks, Mathematical biology, Chaotic Dynamics, Nonlinear Elliptic Partial Differential Equations, Nonlinear Hyperbolic Partial Differential Equations, Fluid Mechanics, Quantum Mechanics, Classical Mechanics. - Recent Research Projects:

- Spatial entropy of multi-dimensional symbolic dynamical system--Song-Sun Lin (NSC 105-2115-M-009-001-)
- Chaotic dynamics for nonhyperbolic systems--Ming-Chia Li (NSC 104-2115-M-009-003-MY2)
- The Effect of Risk Assessments and Immunization Strategies on Multiple-Route Epidemic Spreading Models -- Juang Jouq (NSC 105-2115-M-009-002-MY2)
- Multiplicative integer dynamical systems--Song-Sun Lin (NSC 104-2115-M-009-004-)

Top
- Members:
- Discrete Mathematics and Optimization

- Members:

Chiu-Yuan Chen, Chih-Wen Weng, Hung-Lin Fu, Michael Fuchs. - Topics:

Combinatorial Optimization, Communication Networks, Algorithms, Analysis of Algorithms, Graph Theory, Algebraic Combinatorics, Finite Geometry, Combinatorial Designs, Analytic Combinatorics. - Recent Research Projects:

- The application of graph theory to belt barrier coverage, hole healing, and data collection in wireless sensor networks -- Chiu-Yuan Chen (NSC 105-2115-M-009-012-)
- On Bipartite Graphs Analogue of Brualdi-Hoffman Conjecture -- Chih-Wen Weng (NSC 105-2115-M-009-014-MY2)
- Group Testing And Its Applications (III) -- Hung-Lin Fu (NSC 105-2115-M-009-013-)
- Equitable colorings of graph powers -- Wu-Hsiung Lin (NSC 105-2115-M-009-007-)

Top
- Members:
- Number Theory, Geometry and Analysis

- Members:

Yi-Fan Yang, Shiah-Sen Wang, Michael Fuchs, Yi-Jung Hsu, Kuo-Zhong Wang, Ming-Hsuan Kang, Chi-Hin Chan , Daniel E. Spector . - Topics:

Matrix Analysis, Operator Theory, Numerical Range, Metric Number Theory. - Recent Research Projects:

- Automorphic forms on Shimura curves and their related problems -- Yi-Fan Yang (NSC 102-2115-M-009-001-MY4)
- Discrete Probability Theory, Analytic Combinatorics And Phylogenetics -- Michael Fuchs (NSC 103-2115-M-009-007-MY2)
- The Shape of Random Digital Structures -- Michael Fuchs (NSC 105-2115-M-009-010-MY2)
- Product of two positive semidefinite contractions -- Kuo-Zhong Wang (NSC 105-2115-M-009-003-)
- Riemann Hypothesis on uniform lattices and non-unifom lattices on local classical groups -- Ming-Hsuan Kang (NSC 104-2115-M-009-006-MY2)
- Fractional Gradient PDE and Inequalities--Daniel E. Spector (NSC 105-2115-M-009-004-MY2)

Top
- Members: