In mathematics, the institute develops research in the following fields:

The research in **calculus of variations and differential equations** is triggered by problems coming from geometry, physical sciences, natural sciences or engineering which cannot be solved explicitly in general. The research deals with the existence, uniqueness, regularity and symmetry of these problems solutions.

The research in algebra is focused on **group theory**.

The research in **category theory, **an abstract branch of mathematics, has many interactions with other domains such as algebra, logic, algebraic topology, algebraic geometry, and theoretical computer science. At the IRMP the research in category theory is mainly concerned with the algebraic and geometric aspects of the theory.

The **algebraic topology** is the study of the structures and properties of spaces which are invariant under continuous deformation. The research concerns mainly the development and the geometric applications of rational homotopy which is one of the best algebraic modelizations of spaces. The emphasis is on applications to differential topology.

Research in **geometry and mathematical physics** is described on the page **GPP** .

Members of the institute also pursue research in **mathematics education** and the **history of science**.

### Faculty members

Pierre-Emmanuel CAPRACE

Marino GRAN

Pascal LAMBRECHTS

Timothée MARQUIS

Heiner OLBERMANN

Augusto PONCE

Tim VAN DER LINDEN

Jean VAN SCHAFTINGEN

Pedro VAZ

Enrico VITALE