Research in NCTU-AM

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• Mathematical Modeling and Scientific Computing
• Financial Engineering and Probability
• Differential Equations and Dynamical Systems
• Discrete Mathematics and Optimization
• Number Theory, Geometry and Analysis

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, Yung-Ta Li, Chun-Hao Teng.
  • Topics:
    Large-Scale Matrix Computations, Numerical PDES, Computational Fluid Mechanics, Interface Problems, Porous Media, Fractured Media Problems, Computational Conformal Geometry.
  • Recent Research Projects:
    
    • Nonlinear Matrix Equations and its Applications in Nano Research -- Wen-Wei Lin (NSC 100-2115-M-009 -010 –MY3)
    • Interfacial flows with surfactant -- Ming-Chih Lai (NSC 98-2115-M-009 -014 –MY3)
    • Frontier research and development in industrial and applied mathematics -- Ming-Chih Lai (101-2911-I-009 -509)
    • Research development od mathematics and statatics division -- Ming-Chih Lai (NSC 101-2114-M-009 -001)
    • Mathematical Models and Analysis on Biological Rhythms -- Chih-Wen Shih (NSC 101-2115-M-009-002-MY2)
    • Numerical error analysis for elliptic and parabolic equations in highly heterogeneous media -- Li-Ming Yeh (NSC 99-2115-M-009 -009 –MY2)
    • On the reconstruction of rafraction and reflection free-form surface using FEM and its applications -- Chin-Tien Wu (NSC 101-2115-M-009-003)
    • Nonlinear eigenvalue problems for the distribution of optimal partitions -- Shu-Ming Chang (NSC 101-2115-M-009-009)
    • Boundary value probelms for the shallow water equations of the atmosphere with moisture and Convection -- Ming-Cheng Shiue (NSC 100-2115-M-009 -009 –MY2)
    • Some large-scale matrix computation problems arising in surface parameterization -- Yung-Ta Li (NSC 101-2115-M-009-006)
    • A novel pseudospectral frequency-domain method for solving optical waveguide modes -- Chun-Hao Teng (NSC 99-2115-M-009 -012 –MY3)
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• Financial Engineering and Probability
  
  • Members:
    Yuan-Chung Sheu, Ching-Tang Wu, Michael Fuchs, Guan-Yu Chen, Lo-Bin Chang.
  • Topics:
    Probability Theory and Its Applications, Contingent Claims Pricing, Credit Risk Modeling, Randomized Algorithms, Markov Chains.
  • Recent Research Projects:
    
    • Gerber-Shiu Functions with Applications to Finance and Insurance -- Yuan-Chung Sheu (NSC 101-2115-M-009-013)
    • The entropy mixing of reversible Markov chains -- Guan-Yu Chen (NSC 100-2115-M-009 -003 –MY2)
    • Conditional modeling and hierarchical representations in image analysis -- Lo-Bin Chang (NSC 100-2115-M-009 -007 –MY2)
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• Differential Equations and Dyanmical Systems
  
  • Members:
    Song-Sun Lin, Wen-Wei Lin, Chin-Wen Shin, Ming-Chia Li, C. K. Lin, Juang Jouq, Jong-Eao Lee, Fu-Shiang P. Tsen, Shu-Ming Chang, Chi-Jer Yu.
  • 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:
    
    • Mixing Property and Ergodic Theory of Multi-Dimensional Shift -- Song-Sun Lin (NSC 101-2115-M-009-007-MY2)
    • Nonlinear Matrix Equations and its Applications in Nano Research -- Wen-Wei Lin (NSC 100-2115-M-009 -010 –MY3)
    • Mathematical Models and Analysis on Biological Rhythms -- Chin-Wen Shin (NSC 101-2115-M-009-002-MY2)
    • Chaotic dynamics of high-dimensional systems perturbed from low-dimensional ones -- Ming-Chia Li (NSC 99-2115-M-009 -004 –MY2)
    • Klein-Gordon equation with electromagnetic field -- C. K. Lin (NSC 101-2115-M-009-008-MY2)
    • Stochastically Coupled Maps -- Juang Jouq (NSC 101-2115-M-009-011-MY2)
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• 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 applications of graph theory to wireless networks -- Chiu-Yuan Chen (NSC 100-2115-M-009 -004 –MY2)
    • Combinatorial Design and Its Applications -- Chih-Wen Weng (NSC 99-2115-M-009 -005 –MY3)
    • Combinatorics and Discrete Models -- Hung-Lin Fu (NSC 100-2115-M-009 -005 –MY3)
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• Number Theory, Geometry and Analysis
  
  • Members:
    PeiYuan Wu, Yi-Fan Yang, Shiah-Sen Wang, Chi-Kaung Pai, Michael Fuchs, Yi-Jung Hsu, Kuo-Zhong Wang, Ming-Hsuan Kang.
  • Topics:
    Matrix Analysis, Operator Theory, Numerical Range, Metric Number Theory.
  • Recent Research Projects:
    
    • Numerical ranges of tensor products -- Pei-Yuan Wu (NSC 101-2115-M-009-004)
    • Partition function, Shimura correspondence, quaternary theta series, and special values of L-functions -- Yi-Fan Yang (NSC 99-2115-M-009 -011 –MY3)
    • Metric inhomogeneous Diophantine approximation for formal Laurent series -- Michael Fuchs (NSC 101-2115-M-009-010)
    • Compactness of analytic functions of essentially normal C0 contractions -- Kuo-Zhong Wang (NSC 99-2115-M-009 -013 –MY2)
    • Zeta functions and cohomology of complexes from p-adic reductive groups -- Ming-Hsuan Kang (NSC 100-2115-M-009 -008 –MY2)
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