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Mathematics

D-Index
40
Citations
6953
World Ranking
2050
National Ranking
868

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society

Overview

Michael F. Singer is affiliated with North Carolina State University in the United States and conducts research primarily in the fields of Mathematics and Computer Science. Their work spans various subfields, including Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics, and Applied Mathematics.

The main research topics addressed by Michael F. Singer include Polynomial and algebraic computation, Algebraic Geometry and Number Theory, Nonlinear Waves and Solitons, Advanced Combinatorial Mathematics, Mathematical Dynamics and Fractals, History and Theory of Mathematics, and Advanced Numerical Analysis Techniques.

Recent publications highlight a focus on the mathematical analysis of walks in the quarter plane, differential algebraic generating series, and telescopers for differential forms. Notable papers include:

  • "Walks in the quarter plane: Genus zero case" (2020), published in Journal of Combinatorial Theory Series A
  • "Some structural results on D -finite functions" (2020), published in Advances in Applied Mathematics
  • "On differentially algebraic generating series for walks in the quarter plane" (2021), published in Selecta Mathematica
  • "On the Kernel Curves Associated with Walks in the Quarter Plane" (2021), published in Springer proceedings in mathematics & statistics
  • "Telescopers for differential forms with one parameter" (2024), published in Selecta Mathematica

Michael F. Singer has collaborated frequently with several researchers, including Charlotte Hardouin, Julien Roques, Shaoshi Chen, Ruyong Feng, and Thomas Dreyfus. These collaborations demonstrate ongoing engagement with peers working on interconnected topics.

Their work has been disseminated through notable publication venues such as arXiv (Cornell University), Selecta Mathematica, Journal of Combinatorial Theory Series A, Advances in Applied Mathematics, and Springer proceedings in mathematics & statistics.

Michael F. Singer was recognized as a Fellow of the American Mathematical Society in 2013, reflecting a formal acknowledgment within the professional community.

Best Publications

  • Galois theory of linear differential equations

    Marius van der Put;Michael F. Singer

  • Spectral asymmetry and Riemannian geometry. II

    Unknown

  • Elementary first integrals of differential equations

    M. J. Prelle;M. F. Singer

  • Liouvillian first integrals of differential equations

    Michael F. Singer

  • Galois Theory of Difference Equations

    Marius van der Put;Michael F. Singer

  • Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations

    Michael F. Singer

  • Galois groups of second and third order linear differential equations

    Michael F. Singer;Felix Ulmer

  • Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields

    Dima Yu Grigoriev;Marek Karpinski;Michael F. Singer

  • Differential Galois theory of linear difference equations

    Charlotte Hardouin;Michael F. Singer

  • Testing reducibility of linear differential operators: A group theoretic perspective

    Michael F. Singer

  • Solving Difference Equations in Finite Terms

    P.A. Hendricks;M.F. Singer

  • Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients

    Michael F. Singer

  • Liouvillian and algebraic solutions of second and third order linear differential equations

    Michael F. Singer;Felix Ulmer

  • Extremal metrics on blowups

    Claudio Arezzo;Frank Pacard;Michael F. Singer

  • Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups

    Phyllis J. Cassidy;Michael F. Singer

  • A KUMMER-TYPE CONSTRUCTION OF SELF-DUAL 4-MANIFOLDS

    Claude LeBrun;Michael Singer

  • Formal solutions of differential equations

    Michael. F Singer

  • The model theory of ordered differential fields

    Michael F. Singer

  • Solving homogeneous linear differential equations in terms of second order linear differential equations

    Michael F. Singer

  • Solving ordinary differential equations in terms of series with real exponents

    D. Yu. Grigor′ev;M. F. Singer

  • Necessary conditions for liouvillian solutions of (third order) linear differential equations

    Michael F. Singer;Felix Ulmer

Frequent Co-Authors

Marek Karpinski
Marek Karpinski University of Bonn
Andrew Chi-Chih Yao
Andrew Chi-Chih Yao Tsinghua University
Erich Kaltofen
Erich Kaltofen North Carolina State University
Lou van den Dries
Lou van den Dries University of Illinois at Urbana-Champaign

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