Research Groups
The Department of Mathematics at the University of California, Riverside, is home to a vibrant and diverse research community spanning a broad spectrum of mathematical disciplines. Our faculty members are organized into four primary research groups—Algebra, Analysis, Geometry and Topology, and Partial Differential Equations & Applied Mathematics—each contributing to the advancement of both pure and applied mathematics through innovative research, interdisciplinary collaboration, and mentorship of graduate students.
Each research group is composed of faculty scholars whose profiles can be explored in the sections below. Together, these groups foster a dynamic environment that supports fundamental discovery and addresses complex real-world problems through mathematical insight.
Faculty Activities
- Commutative Algebra
- Representation Theory
- Combinatorics
- Combinatoric Number Theory
- Algebraic Geometry
Research Activities
- Harmonic Analysis
- Functional Analysis
- Partial Differential Equations
- Operator Algebras
- Several Complex Variables
- Probability Theory
- Mathematical Physics
- Approximation Theory
- Fractal Geometry and Dynamical Systems
Research Activities
- Algebraic Topology
- Low Dimension Topology
- Geometric Topology
- Differential Topology
- Transformation Groups
- Riemannian Geometry
- Complex Differential Geometry
- Geometric Analysis
Subgroups and Research Activities
- Mathematical Biology
- Multi-scale Mathematical Modeling
- Computational Mathematics
- Scientific Computing
- Modeling of fluids
- Partial Differential Equations
- Optimization
- Machine Learning
- Inverse Problems
- Image Processing
- Computational Methods for nonlinear differential equations