Research in nycu-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 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:
    Ming-Chih Lai, Chih-Wen Shih, Juang Jonq, 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:
    
    • 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(2/3)-- Chin-Tien Wu (113-2115-M-A49-002)
    • About the rigidity of stationary Navier-Stokes flows on a punctured hyperbolic space -- Chi-Hin Chan (113-2115-M-A49-008-MY2)
    • 數據驅動之數學建模--Te-Sheng Lin (111-2628-M-A49-008-MY4)
    • Solving PDEs by neural networks--Ming-Chih Lai (113-2115-M-A49-014-MY3)
    • Synchronized and Chaotic Dynamics of Coupled Lattices System Driven by a Parameter of Oscillators and Applications to Biomedical Sciences -- Juang Jonq (113-2115-M-A49-007-)
    • How Phase-Isostable Reduction Captures the Oscillations -- Chih-Wen Shih (113-2115-M-A49-006-MY2)
    • Investigating Quantum Channels in Noisy Quantum Systems: Some Mathematical Problems in Quantum Information Theory -- Cheng-Fang Su(113-2115-M-A49-015-MY2)
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• Financial Engineering and Probability
  
  • Members:
    Yuan-Chung Sheu,Guan-Yu Chen, Yuh-Jye Lee、 Xiang Fang、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 (III) -- Yuan-Chung Sheu (113-2115-M-A49-009- )
    • The spectral analysis of random walks on cycles -- Guan-Yu Chen (113-2115-M-A49-010-MY2 )
    • Problems in Banach Spaces of Random Analytic Functions -- Xiang Fang (112-2115-M-A49-013-MY2 )
    • Study on frog model -- Yuki Chino (111-2115-M-A49-009-MY3)
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• Differential Equations and Dyanmical Systems
  
  • Members:
    Chin-Wen Shin, Ming-Chia Li, Juang Jouq, Shu-Ming Chang, Chi-Jer Yu, Chi-Hin Chan , Hsin-Yuan Huang, Chang-Hong Wu ,Catalin Carstea,Yi-Hsuan Lin ,Cheng-Fang Su.
  • 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:
    
    • On polynomial coefficients and solutions for linear differential equations and machine-learning solver -- Ming-Chia Li (113-2115-M-A49-005-)
    • How Phase-Isostable Reduction Captures the Oscillations -- Chin-Wen Shin (113-2115-M-A49-006-MY2)
    • Propagation phenomena and evolutionary dynamics in mathematical models -- Chang-Hong Wu (113-2628-M-A49-004-MY4)
    • Linear, local, non-linear and non-local inverse problems for partial differential equations--Yi-Hsuan Lin(113-2115-M-A49-017-MY3)
    • Inverse problems in nonlinear and nonlocal equations: Theory and application(5/5)--Yi-Hsuan Lin(113-2628-M-A49-003-)
    • Investigating Quantum Channels in Noisy Quantum Systems: Some Mathematical Problems in Quantum Information Theory -- Cheng-Fang Su(113-2115-M-A49-015-MY2)
    • Topics on the nonlinear evolutionary partial differential equations -- Hsin-Yuan Huang (111-2115-M-A49-016-MY5)
    • About the rigidity of stationary Navier-Stokes flows on a punctured hyperbolic space -- Chi-Hin Chan (113-2115-M-A49-008-MY2)
    • Synchronized and Chaotic Dynamics of Coupled Lattices System Driven by a Parameter of Oscillators and Applications to Biomedical Sciences -- Juang Jouq (113-2115-M-A49-007-)
    • Inverse problems for elliptic and parabolic equations with anisotropy or quasilinear nonlinearity -- Catalin Carstea (113-2115-M-A49-018-MY3)
    • Investigating Quantum Channels in Noisy Quantum Systems: Some Mathematical Problems in Quantum Information Theory -- Cheng-Fang Su(113-2115-M-A49-015-MY2)
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• 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 model and graph algorithm for the minimum cost noncrossing flow problem in layered networks with applications to quay crane scheduling -- Chiu-Yuan Chen (113-2115-M-A49-012-MY2)
    • A class of distance-regular graphs -- Chih-Wen Weng (113-2115-M-A49-011-MY2)
    • On the well-coveredness of block-cactus graphs -- Wu-Hsiung Lin (113-2115-M-A49-013-)
    • Varchenko-Gelfand Filtration in Tropical Geometry -- Chi-Ho YUEN (113-2115-M-A49-004-MY2)
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• Number Theory, Geometry and Analysis
  
  • Members:
    Shiah-Sen Wang, Kuo-Zhong Wang, Xiang Fang,Ming-Hsuan Kang, Chi-Hin Chan , Ye-Kai Wang ,Sz-Sheng Wang ,Cheng-Fang Su.
  • Topics:
    Matrix Analysis, Operator Theory, Numerical Range, Metric Number Theory,Contact Geometry.
  • Recent Research Projects:
    
    • Exploring the Zeta Function of Discrete Subgroups --Ming-Hsuan Kang (112-2115-M-A49-006-MY2)
    • Numerical Ranges of Finite Matrices --Kuo-Zhong Wang (112-2115-M-A49-003-MY2)
    • Problems in Banach Spaces of Random Analytic Functions -- Xiang Fang (112-2115-M-A49-013-MY2 )
    • About the rigidity of stationary Navier-Stokes flows on a punctured hyperbolic space -- Chi-Hin Chan (113-2115-M-A49-008-MY2)
    • Bartnik static extension problem --Ye-Kai Wang (112-2115-M-A49-009-MY2)
    • Investigating Quantum Channels in Noisy Quantum Systems: Some Mathematical Problems in Quantum Information Theory -- Cheng-Fang Su(113-2115-M-A49-015-MY2)
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