Research Areas

The Department has an international reputation as an outstanding center for research.

Visual representation of the E8 group.

Algebra and Representation Theory

Algebraic Geometry

Algebraic Geometry

A frame of an animation of the heat equation with a smiley as the initial condition.

Analysis and PDEs

Node representation update in a Message Passing Neural Network layer.

Applied and Computational Mathematics, Data Science, Machine Learning

Example of b-coloring of the Shrikhande graph : the highlighted nodes are vertices with neighbors in each other's colors.

Combinatorics

Commutative Algebra

Commutative Algebra

Diagram depicting how right multiplication takes horizontal subspaces into each other on a principal bundle.

Geometry and Topology

Mathematical Biology

Mathematical Biology

Mathematical Logic and Foundations

Mathematical Logic and Foundations, Model Theory

Mathematical Physics

Mathematical Physics

Mathematics Education

Mathematics Education

Number Theory

Number Theory

Operator Algebras

Operator Algebras

Top left: random sums; Top right: Central Limit Theorem – random sums scaled by n approach Gaussian distribution; Bottom left: Law of the Iterated Logarithm – random sums scaled by n log ⁡ log ⁡ n are bounded in the limit by ± 2; Bottom right: Law of Large Numbers – random sums scaled by n tend to zero.

Probability and Statistics

Quantum Information Science

Quantum Information Science