# 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 , 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:

- Differentiable surface reconstruction from 3D point cloud--Chin-Tien Wu (NSC 107-2115-M-009-004-)
- Fast Solvers for Three-Dimensional Maxwell's Equations on Topological Photonic Crystals(2/4)--Wen-Wei Lin (NSC 107-2119-M-009-014-)
- 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, 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:

- Random walks on random media --Guan-Yu Chen (NSC 107-2628-M-009-005-MY4)
- Some Optimization Problems on Stochastic Portfolio Theory--Yuan-Chung Sheu (NSC 107-2115-M-009-012-)

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- 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:

- Fully Cooperative Coinfection Model -- Juang Jouq (NSC 107-2115-M-009-011-MY2)
- Classifications of maximum meromorphic dynamical Zeta functions--Song-Sun Lin (NSC 107-2115-M-009-006-)

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- 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 study of continuous services of mobile servers and mutual transferability of dominating sets -- Chiu-Yuan Chen (NSC 107-2115-M-009-014-)
- Quasi-spectral Study on Hamiltonian Graphs -- Chih-Wen Weng (NSC 107-2115-M-009-009-MY2)
- Subgraphs in Edge-colored Graphs (II) -- Hung-Lin Fu (NSC 107-2115-M-009-015-)
- Equitable colorings of toroidal graphs -- Wu-Hsiung Lin (NSC 107-2115-M-009-007-)

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- 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:

- Stochastic Properties of Phylogenetic Trees and Networks -- Michael Fuchs (NSC 107-2115-M-009-010-MY2)
- Numerical range of the generalized Aluthge transform of a matrix -- Kuo-Zhong Wang (NSC 107-2115-M-009-001-)
- L^1 Inequalities --Daniel E. Spector (NSC 107-2115-M-009-002-MY2)

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- Members: