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.

Faculty 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
Steven Strogatz Dynamical systems applied to physics, biology, and social science.
Nicolas Templier Number theory, automorphic forms, and mathematical physics
Alex Townsend Numerical analysis, scientific computing, and numerical algebraic geometry
Alexander Vladimirsky Numerical methods, dynamical systems, nonlinear PDEs, control theory
Xin Zhou Geometric Analysis and Calculus of Variations

Emeritus and Other Faculty

Ahmed Bou-Rabee Probability, elliptic PDE
Leonard Gross Functional analysis, constructive quantum field theory
John M. Guckenheimer Dynamical systems
Alfred H. Schatz Numerical solutions of partial differential equations
John Smillie Dynamical systems

Activities and Resources:

Related people

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Xiaodong Cao


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Leonard Gross

Professor Emeritus

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John M. Guckenheimer

Abram R. Bullis Professor Emeritus of Mathematics

Image of Daniel Halpern-Leistner
Daniel Halpern-Leistner

Goenka Family Assistant Professor

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Camil Muscalu


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Richard Rand

Professor, Stephen H. Weiss Presidential Fellow

Image of Laurent Saloff-Coste
Laurent Saloff-Coste

Abram R. Bullis Professor of Mathematics

Image of Alfred H. Schatz
Alfred H. Schatz

Professor Emeritus

Image of John Smillie
John Smillie

Professor Emeritus

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Steven Strogatz

Jacob Gould Schurman Professor of Applied Mathematics, Stephen H. Weiss Presidential Fellow

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Xin Zhou

Associate Professor

All research areas

Algebra    Analysis    Applied Mathematics    Combinatorics and Discrete Geometry    Geometry    Logic    Probability and Statistics    Topology