# Research at Department of Mathematics

The mathematical research at Uppsala University covers a large number of fields in both pure and applied mathematics. Our research includes collaborations with other disciplines as well as with industry.

## Our research is organised into the following six research areas:

### Algebra, Logic and Representation Theory

Patterns and structures are the core of algebra and logic. We are conducting research in representation theory, logic, commutative algebra, algebraic geometry and algebraic groups.

### Analysis and Partial Differential Equations

Analysis is one of the first areas of research in mathematics at Uppsala University. Our research today focuses on partial differential equations, geometry, mathematical physics and machine learning.

### Dynamical Systems and Number Theory

Researchers in dynamical systems study the long time behavior of points moving in a geometric space according to a given rule. Some types of dynamical systems have strong links to classical problems in number theory.

### Geometry and Physics

Mathematics and physics have always been closely connected. A mathematical field that develops in direct interaction with physics is symplectic geometry.

### Probability Theory and Combinatorics

This area includes, among other topics, combinatorial probability theory, where researchers use probability theoretical methods to study discrete structures.

### Statistics, AI and Data Science

The central part of this area is analysis of data. Researchers create methods, principles and criteria for processing data from experiments and observations of reality.