# 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 (MOST) distinguished researchership. Almost every faculty member is supported by MOST 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 ,Cheng-Fang Su. - 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 (MOST 108-2115-M-009-002-MY2)
- Fast Solvers for Three-Dimensional Maxwell's Equations on Topological Photonic Crystals(3/4)--Wen-Wei Lin (MOST 108-2119-M-009-006-)
- Mathematical Studies on Neural Field Models -- Chih-Wen Shih (MOST 109-2115-M-009-002-MY2)
- Liquid films on curved substrates --Te-Sheng Lin (MOST 109-2115-M-009-006-MY2)
- Anthesis of the Stokes paradox on the hyperbolic plane -- Chan Chi Hin (MOST 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、Yuki Chino. - 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 (MOST 107-2628-M-009-005-MY4)
- Some Problems on Convergence and Stability of Blaschke unwinding for random functions (II)--Yuan-Chung Sheu (MOST 109-2115-M-009-011-)
- The study of the affection of random environment to self-avoiding walk --Yuki Chino (MOST 109-2115-M-009-013-MY2)

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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 , Cheng-Fang Su, 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, Quantum Computing, Classical Mechanics. - Recent Research Projects:

- Fast Solvers for Three-Dimensional Maxwell's Equations on Topological Photonic Crystals(4/4) -- Wen-Wei Lin(MOST 109-2123-M-009-002-)
- Dynamics of Annual Influenza Models(1/2) -- Juang Jouq (MOST 109-2115-M-009-008-)
- Phase-locked Solutions in Coupled System -- Chin-Wen Shin (MOST 107-2115-M-009-003-MY2)
- A note on the Banach mapping theorem and its related conjecture -- Ming-Chia Li (MOST 109-2115-M-009-003-MY2 )
- Wave propagation arising in mathematical biology(4/4) -- Chang-Hong Wu (MOST 110-2636-M-009-006--)
- Inverse problems in nonlinear and nonlocal equations: Theory and application(1/5) (MOST 109-2636-M-009-006) -- Yi-Hsuan Lin
- Study of Viscous effect for N. S. flows on ellipsoid -- Chi-Hin Chan (MOST 109-2115-M-009-009-MY2)

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- Members:
- Discrete Mathematics and Optimization

- Members:

Chiu-Yuan Chen, Chih-Wen Weng, Wu-Hsiung Lin. - Topics:

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

- The shortest Hamiltonian cycle problem in graph theory and its application to charging tour scheduling problem in wireless rechargeable sensor networks -- Chiu-Yuan Chen (MOST 109-2115-M-009-010)
- Dirac-type Study of Hamiltonian Graphs -- Chih-Wen Weng (MOST 109-2115-M-009-007-MY2 )
- Graph isomorphic classification of shifted toroidal grids -- Wu-Hsiung Lin (MOST 109-2115-M-009-005- )

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- Members:
- Number Theory, Geometry and Analysis

- Members:

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

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

- The powers of a numerical contraction -- Kuo-Zhong Wang (MOST 109-2115-M-009-001- )
- Factorization of Affine Weyl Groups from Iwahori Hecke Algebra -- Ming-Hsuan Kang (MOST 108-2115-M-009-007-MY2)

- Members: