# Geometry and topology

People have for a long time been interested in the properties of geometric shapes. In geometry one is usually interested in terms like distance, angle, area and volume. Topologists study the qualitative properties of geometric space. As the math has evolved, geometry and topology have grown to an active research area with links to physics and many other parts of mathematics.

## About the group

The Faculty of Mathematics and Natural Sciences has selected the research group in Geometry and Topology as an emphasized research area, or more specifically as an "emerging top-tier research group". A large part of the group's research concentrates on algebraic topology and algebraic K-theory, with applications to geometric topology. The group is also involved in relating homotopy theory at large to other subjects. Motivic homotopy theory is an in vogue example of a homotopy theory that arises in algebraic geometry. An emerging example is a new homotopy theory of C*-algebras. Members of the group are also doing research related to Floer homology, manifolds of dimension 4 and symplectic geometry.

## Projects

Equations in Motivic Homotopy, 2021-2025: Funded by RCN, this project aims at studying motivic homotopy theory, a relatively new subject that allows us to utilize algebraic topology methods to understand the objects of interest in algebraic geometry.

~~Motivic Hopf Equation, 2016 -2020:~~ This is a project funded of RCN. The research aims at formulating and solving ground-breaking problems in motivic homotopy theory. As a relatively new field of research this subject has quickly turned into a well-established area of mathematics drawing inspiration from both algebra and topology.

## Cooperation

- Topology at the University of Bergen
- Geometry and Topology at NTNU
- Topology at the University of Copenhagen
- Topology(CTQM) at Aarhus University

## Academic programmes and courses

Bachelor program:

Mathematics, Natural Sciences, Technology

Master program:

Mathematics

Courses:

MAT3500/4500 - Topology

MAT4510 - Geometric structures

MAT 4520/9520 Manifolds

MAT 4530/9530 Algebraic topology I

MAT 4540/9540 Algebraic topology II

MAT 4551/9551 Symplectic geometry

MAT 9560 Lie groups

MAT 9570 Algebraic K-theory

MAT 9580 Algebraic topology III

MAT 4590/9590 Differential geometry

MAT 4595/9595 Geometry and analysis