Research areas
The department spans a broad range of mathematics, with active research groups and strong connections across fields and to physics, computer science, and biology.
Algebra & Number TheoryNumber theory explores the properties of integers and related structures using tools from analysis, algebra, and topology. It is one of the oldest and most beautiful areas of mathematics, with connections to geometry, cryptography, and many other fields. Learn more → | AnalysisAnalysis studies functions, equations, and mathematical structures using methods of approximation, continuity, and limiting processes. It is a broad and fundamental area of mathematics, with connections to geometry, probability, physics, and many other fields. Learn more → |
CombinatoricsCombinatorics investigates discrete structures and counting problems using algebraic, analytic, and geometric methods. It is a broad and active area of mathematics, with connections to algebra, topology, geometry, number theory, and computer science. Learn more → | GeometryGeometry examines the properties of shapes and spaces using techniques from analysis, topology, and algebra. It is a broad and fundamental area of mathematics, with connections to quantum field theory, string theory, and many other fields. Learn more → |
Probability, Ergodic Theory & Mathematical PhysicsProbability theory develops rigorous frameworks for random phenomena and uncertainty using tools from analysis, combinatorics, and dynamical systems. It is a broad and fundamental area of mathematics, with connections to statistical mechanics, physics, biology, and many other fields. Learn more → | TopologyTopology concerns the properties of spaces preserved under continuous deformation, approached through algebraic and geometric methods. It is a broad and fundamental area of mathematics, with connections to analysis, geometry, physics, and many other fields. Learn more → |