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Research statement

Research mission

To become the world-leading centre in quantum geometry of moduli spaces at the crucial interface between mathematics and theoretical physics, with the aim to contribute to the mathematical underpinnings of contemporary and future physical theories.

Scientific context

The role of mathematics in our understanding of nature has been recognized for millennia. Its importance is especially poignant in modern theoretical physics as the cost of experiments escalates and the mathematical complexity of physical theories increases.

Major challenges

• To participate in defining quantum field theory as a mathematical entity.

• To unify quantum theory with gravity.

Conceptual goals

• To significantly advance the understanding of moduli spaces and their quantization.

• To train the next generation of scholars and researchers to build the centre into a world-renowned catalyst of collaborative, cutting-edge research

Specifically: To develop the quantum geometry of moduli spaces so as to provide complete, mathematical models for a number of quantum field theories.

Main research focus

• The Geometric Langlands Program and Higgs' bundle Moduli Spaces

• Toeplitz operators and geometric quantization of moduli spaces

• Combinatorial models for moduli spaces and quantum moduli spaces

• Quantum representation theory and perturbative invariants

Possible spin-off applications

• The protein folding problem in Biology

• Quantum computing in computer science/physics

Read about the organisation of QGM