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Grantor: Australian Research Council

**Objectives**:

Higher category theory is a very young branch of mathematics (less then 20 years old), which has already became a vital tool in many areas of mathematics and theoretical physics such as algebra, geometry, topology, mathematical logic, quantum field theory and computer science. The impact of higher category theory for the future development of mathematics and physics will be immense. In its present shape, however, this theory is technically very difficult. The challenge is to find an approach to this theory which would allow to make it transparent and accessible for the wider scientific community. In our project we are going to propose such an approach and we will study its application to important open problems in geometry and topology.

IM leader :

Main investigator:

**Batanin** Michael

Participating institutions:

Mathematics Department, Macquarie University, Sydney, **Coordinator**

Institute of Mathematics, Czech Academy of Sciences

Université de Nice-Sophia Antipolis, Nice, Laboratoire J.A. Dieudonné