# 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, Yung-Ta Li, Chi-Hin Chan , Daniel E. Spector Te-Sheng Lin . - Topics:

Large-Scale Matrix Computations, Numerical PDES, Computational Fluid Mechanics, Interface Problems, Porous Media, Fractured Media Problems, Computational Conformal Geometry. - Recent Research Projects:

- Computational Conformal Geometry and Its Applications (2/4)--Wen-Wei Lin (NSC 103-2628-M-009-005)
- Frontier research and development in industrial and applied mathematics -- Ming-Chih Lai (101-2911-I-009 -509)
- Research Developent And Promotion Of Mathematics Division -- Ming-Chih Lai (NSC 103-2114-M-009-001)
- Dynamics And Oscillations In Coupled Systems -- Chih-Wen Shih (NSC 103-2115-M-009-002-MY2)
- Regularity Of Non-Uniform Elliptic And Non-Uniform Parabolic Equations In Periodic Heterogeneous Media--Li-Ming Yeh (NSC 103-2115-M-009-014)
- Application Of Freeform Design In Imaging Optics -- Chin-Tien Wu (NSC 103-2115-M-009-003)
- Computing Discrete Sufrace Ricci Flows -- Shu-Ming Chang (NSC 102-2115-M-009-012)
- Numerical computation and analysis of the mathematical problems in geophysical fluid mechanics -- Ming-Cheng Shiue (NSC 102-2115-M-009-015-MY2)
- The De-Giorgi's Method As Applied In The Study Of Regularity Of Solutions To Hamilton-Jacobi's -- Chan Chi Hin (NSC 103-2115-M-009-010-MY2)

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- Members:
- Financial Engineering and Probability

- Members:

Yuan-Chung Sheu, Michael Fuchs, Guan-Yu Chen. - Topics:

Probability Theory and Its Applications, Contingent Claims Pricing, Credit Risk Modeling, Randomized Algorithms, Markov Chains. - Recent Research Projects:

- Stochastic Models With Jumps And Applications-- Yuan-Chung Sheu (NSC 103-2115-M-009-009)
- The L2 Cutoff Time For Birth And Death Processes -- Guan-Yu Chen (NSC 103-2115-M-009-011)

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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:

- Natural Measure Of Multi-Dimensional Shifts -- Song-Sun Lin (NSC 103-2115-M-009-004)
- Symbolic embedding and globla implicit function theorem, II -- Ming-Chia Li (NSC 102-2115-M-009-008-MY2)
- Cluster Synchronization And Synchronized Dynamics In Networks Of Neurons With Chemical Synaped -- Juang Jouq (NSC 103-2115-M-009-008-MY2)

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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:

- Distance-Two Coloring For The Adjacency Graphs Of Wireless Sensor Networks -- Chiu-Yuan Chen (NSC 103-2115-M-009-012)
- Linear Algebra Applied to Graph Theory -- Chih-Wen Weng (NSC 102-2115-M-009-009-MY3)
- Group Testing And Its Applications -- Hung-Lin Fu (NSC 103-2115-M-009-013)

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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:

- Automorphic forms on Shimura curves and their related problems -- Yi-Fan Yang (NSC 102-2115-M-009-001-MY4)
- Discrete Probability Theory, Analytic Combinatorics And Phylogenetics -- Michael Fuchs (NSC 103-2115-M-009-007-MY2)
- Numerical Ranges Of Tensor Product Matrices -- Kuo-Zhong Wang (NSC 103-2115-M-009-001)
- On The P-adic And Complex Dual Groups -- Ming-Hsuan Kang (NSC 103-2115-M-009-006)

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- Members: