# 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 and Technology Council (NSTC) distinguished researchership. Alevery faculty member is supported by 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:

- Time-harmonic Maxwell's equations in periodic micro-structures -- Li-Ming Yeh (112-2115-M-A49-008- )
- Analysis and computation of ice sheet dynamics based on deep learning algorithms -- Ming-Cheng Shiue (112-2115-M-A49-012-MY2 )
- Error Covariance estimation in real time computing for the gimbal control and UAV tracking(1/3) --Chin-Tien Wu (112-2115-M-A49-011-)
- About the proper expression for the Navier stokes equations on a surface -- Chi-Hin Chan (111-2115-M-A49-012-MY2)
- 數據驅動的數學建模 --Te-Sheng Lin (111-2628-M-A49-008-MY4)
- Research on fluid interface problems -- Ming-Chih Lai (110-2115-M-A49-011-MY3)
- Incorporating Economic Constraints for Optimal Control of Immunizing Infections(2/2) -- Juang Jonq (112-2115-M-A49-001-)
- Mathematical Analysis on Coupled-cell Systems -- Chih-Wen Shih (111-2115-M-A49-011-MY2)
- Inverse problems for equations featuring anisotropy, nonlinearity, or randomness -- Catalin Carstea (112-2115-M-A49-002-)
- Mathematical research topics in quantum computing -- Cheng-Fang Su (111-2115-M-A49-010-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:

- Neural Activation Scattering Transform for Random Inputs and its Applications (II) --Yuan-Chung Sheu (112-2115-M-A49-007-)
- The spectral analysis of random walks on cycles --Guan-Yu Chen (111-2115-M-A49-015-MY2)
- Study on frog model --Yuki Chino (111-2115-M-A49-009-MY3)

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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:

- 最佳傳輸方法在3D醫學影像分割技術的應用(2/2)-- Wen-Wei Lin (111-2115-M-A49-018-)
- Incorporating Economic Constraints for Optimal Control of Immunizing Infections(1/2) -- Juang Jonq (111-2115-M-A49-014-)
- Mathematical Analysis on Coupled-cell Systems -- Chih-Wen Shih (111-2115-M-A49-011-MY2)
- The hyperbolicity of stretch across and its application -- Ming-Chia Li (111-2115-M-A49-013-MY2)
- Qualitative analysis and application for reaction-diffusion systems -- Chang-Hong Wu (111-2115-M-A49-003-MY3)
- Inverse problems in nonlinear and nonlocal equations: Theory and application(4/5) (112-2628-M-A49-002-) -- Yi-Hsuan Lin
- Inverse problems in nonlinear and nonlocal equations: Theory and application(5/5) (113-2628-M-A49-002-) -- Yi-Hsuan Lin
- About the proper expression for the Navier stokes equations on a surface -- Chi-Hin Chan (111-2115-M-A49-012-MY2)
- Mathematical research topics in quantum computing -- Cheng-Fang Su (111-2115-M-A49-010-MY2)

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- Members:
- Discrete Mathematics and Optimization

- Members:

Chiu-Yuan Chen, Chih-Wen Weng, Wu-Hsiung Lin,Chi-Ho YUEN. - 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:

- Graph theory and its application to the superposed data uploading problem in IoT with smart devices -- Chiu-Yuan Chen (111-2115-M-A49-006-MY2 )
- The alpha spectral radius of a graph -- Chih-Wen Weng (111-2115-M-A49-005-MY2)
- The signed domination number of shifted toroidal grids -- Wu-Hsiung Lin (112-2115-M-A49-005- )

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- Members:
- Number Theory, Geometry and Analysis

- Members:

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

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

- Numerical Ranges of Finite Matrices -- Kuo-Zhong Wang (112-2115-M-A49-003-MY2)
- Exploring the Zeta Function of Discrete Subgroups -- Ming-Hsuan Kang (112-2115-M-A49-006-MY2)
- About the proper expression for the Navier stokes equations on a surface -- Chi-Hin Chan (111-2115-M-A49-012-MY2)
- Bartnik static extension problem -- Ye-Kai Wang (112-2115-M-A49-009-MY2)
- Mathematical research topics in quantum computing -- Cheng-Fang Su (111-2115-M-A49-010-MY2)

- Members: