# Research

Mathematics can be described as the science which, using logic, investigates properties and patterns of abstract structures.

Historically, mathematics has developed in close interplay with the natural sciences and technology. In modern mathematics, questions from within the field itself are studied, as well as a broad spectrum of questions motivated by applications in natural and social sciences. Mathematics continues to be the fundamental tool and language of science.

At the Division of Mathematics, research is conducted in many different areas of modern mathematics. In particular, there are research groups in the areas of algebra and algebraic geometry, algebraic topology, combinatorics, differential geometry, dynamical systems, harmonic analysis, mathematical physics, number theory, and partial differential equations. Examples of applications inspiring research at the division are image reconstruction and artificial intelligens. The Division of Mathematics provides first-cycle courses for all students at KTH. Among others, the courses in algebra and geometry, and single- and multivariable calculus, which are part of the basic education of all engineering programs. A broad range of second-cycle courses are given. Together with the Department of Mathematics at Stockholm University, the division is responsible for a masters program in mathematics. At the division there is a broad doctoral program at high international level.

### Our research areas

- Algebraic Geometry & Commutative Algebra
- Algebraic Topology
- Algorithms and Complexity
- Combinatorics
- Complex and Harmonic Analysis
- Differential Geometry & General Relativity
- Dynamical Systems
- Mathematical Image Science
- Number Theory
- Partial Differential Equations
- Probability (Random Matrices, Random Conformal Geometry)