Mathematical analysis covers a wide range of different subjects. Areas currently active at Cornell include: dynamics, harmonic analysis, potential analysis, partial differential equations, geometric analysis, applied analysis, and numerical methods. In addition, we value the many interactions with other areas such as differential geometry, geometry, Lie theory, combinatorics, and probability.

Notable contributions of Cornell faculty to analysis include: Larry Payne’s work on ill-posed problems, Len Gross’s logarithmic Sobolev inequality, Strichartz’s estimates, James Eell’s work on harmonic maps (joint with J. Sampson), and Richard Hamilton’s seminal contribution to the Ricci flow.

**Field Members**

Xiaodong Cao | Differential geometry and geometric analysis |

Timothy J. Healey | Applied analysis and partial differential equations, mathematical continuum mechanics |

John H. Hubbard | Analysis, differential equations, differential geometry |

Camil Muscalu | Harmonic analysis and partial differential equations |

Richard H. Rand | Nonlinear dynamics |

Laurent Saloff-Coste | Analysis, potential theory, probability and stochastic processes |

Robert S. Strichartz | Harmonic analysis, partial differential equations, analysis on fractals |

Steven Strogatz | Dynamical systems applied to physics, biology, and social science. |

Nicolas Templier | Number theory, automorphic forms, and mathematical physics |

Alexander Vladimirsky | Numerical methods, dynamical systems, nonlinear PDEs, control theory |

Emeritus and Other Faculty

Numerical solutions of partial differential equations | |

Federico Fuentes | Finite element analysis, numerical analysis, computational mechanics, applied nonlinear dynamics |

Nataliya Goncharuk | Dynamical systems and differential equations |

Leonard Gross | Functional analysis, constructive quantum field theory |

John M. Guckenheimer | Dynamical systems |

Benjamin Harris | Abstract Harmonic Analysis |

Brian Hwang | Number theory, representation theory, algebraic geometry |

Artem Pulemotov | Geometric analysis |

Alfred H. Schatz | Numerical solutions of partial differential equations |

John Smillie | Dynamical systems |