There are currently ten research groups at IMPA working in the following areas:

- Algebra
- Analysis/Partial Differential Equations
- Computer Graphics
- Fluid Dynamics
- Holomorphic Dynamics and Complex Foliations
- Mathematical Economics
- Differential Geometry
- Optimization
- Probability
- Dynamical Systems and Ergodic Theory

A brief summary follows of the activities being developed in each one of the above-mentioned areas, highlighting their major research endeavors.