# Research in NCTU-AM

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### 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 , 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:

- Blind deconvolution based on prior information --Chin-Tien Wu (NSC 108-2115-M-009-002-MY2)
- Fast Solvers for Three-Dimensional Maxwell's Equations on Topological Photonic Crystals(3/4)--Wen-Wei Lin (NSC 108-2119-M-009-006-)
- Phase-locked Solutions in Coupled System -- Chih-Wen Shih (NSC 107-2115-M-009-003-MY2)
- Bifurcation analysis of electrified falling liquid films--Te-Sheng Lin (NSC 107-2115-M-009-008-MY2)
- Anthesis of the Stokes paradox on the hyperbolic plane -- Chan Chi Hin (NSC 107-2115-M-009-013-MY2)

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- Members:
- Financial Engineering and Probability

- Members:

Yuan-Chung Sheu,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:

- Random walks on random media --Guan-Yu Chen (NSC 107-2628-M-009-005-MY4)
- Some Problems on Convergence and Stability of Blaschke unwiding for random functions--Yuan-Chung Sheu (NSC 108-2115-M-009-008-)

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- Members:
- Differential Equations and Dyanmical Systems

- Members:

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 , Chang-Hong Wu ,Yi-Hsuan Lin . - 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:

- Fully Cooperative Coinfection Model -- Juang Jouq (NSC 107-2115-M-009-011-MY2)
- Phase-locked Solutions in Coupled System -- Chin-Wen Shin (NSC 107-2115-M-009-003-MY2)
- A generalization of the implicit function theorem and detection of chaotic dynamics -- Ming-Chia Li (NSC 108-2115-M-009-004- )
- Wave propagation arising in mathematical biology(3/4) -- Chang-Hong Wu (NSC 109-2636-M-009-008-)
- Inverse problems in nonlinear and nonlocal equations: Theory and application(1/5) (NSC 109-2636-M-009-006) -- Yi-Hsuan Lin

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- Members:
- Discrete Mathematics and Optimization

- Members:

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

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

- The longest path problem and its application in barrier-coverage problem in wireless sensor networks -- Chiu-Yuan Chen (NSC 108-2115-M-009-013-)
- Subgraphs in Edge-colored Graphs (III) -- Hung-Lin Fu (NSC 108-2115-M-009-010- )
- Equitable colorings of Sudha graphs -- Wu-Hsiung Lin (NSC 108-2115-M-009-006- )

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- Members:
- Number Theory, Geometry and Analysis

- Members:

Shiah-Sen Wang, Kuo-Zhong Wang, Ming-Hsuan Kang, Chi-Hin Chan . - Topics:

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

- Numerical ranges of the powers of a matrix -- Kuo-Zhong Wang (NSC 108-2115-M-009-001- )
- Factorization of Affine Weyl Groups from Iwahori Hecke Algebra -- Ming-Hsuan Kang (NSC 108-2115-M-009-007-MY2)

- Members: