Navier-Stokes differential equations used to simulate airflow around an obstruction.

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

Differential geometry and geometric analysis
Applied analysis and partial differential equations, mathematical continuum mechanics
Analysis, differential equations, differential geometry
Harmonic analysis and partial differential equations
Nonlinear dynamics
Analysis, potential theory, probability and stochastic processes
Harmonic analysis, partial differential equations, analysis on fractals
Dynamical systems applied to physics, biology, and social science.
Number theory, automorphic forms, and mathematical physics
Numerical methods, dynamical systems, nonlinear PDEs, control theory

Emeritus and Other Faculty

Numerical solutions of partial differential equations
Complex variables, Teichmüller spaces
Dynamical systems and differential equations
Functional analysis, constructive quantum field theory
Dynamical systems
Number theory, representation theory, algebraic geometry
Numerical solutions of partial differential equations
Dynamical systems

Graduate Students

Harmonic analysis

Activities and Resources