The symbiotic relation between string theory and mathematics has proven to be a gold mine for both fields, providing a guideline for the mathematicians and powerful tools for the physicists.
For example, by extending the newly discovered mathematical concept called generalized complex geometry (GCG) to the supersymmetric sigma model, a new understanding of the mathematics of extended supersymmetric sigma models is being achieved.
On the other hand, generalized complex manifolds have been shown to arise in the context of string theory compactification with fluxes and a better knowledge of the underlying mathematics will lead to powerful tools for the physicists to apply.
The discovery that non-commutative manifolds naturally emerge in the context of string theory led to a burst of activity in the field and to new insight into string dynamics from the study of non(anti)commutative (N(A)C) field theories, which also found applications outside the high energy physics area, for example in the study of the quantum hall effect.
A further example of the relation between string theory and mathematics is provided by the great improvement recently achieved in the study of the AdS/CFT duality, when perspective and tools of the theory of integrable systems were applied to the problem.
A two-year stay at the Department of Theoretical Physics in Uppsala would give me the opportunity to develop new mathematical skills by collaborating with U. Lindstrom in the context of sigma-model theory and N(A)C geometry and with J. Minaha n and K. Zarembo by applying my knowledge of Berkovits string to the AdS/CFT correspondence.
My research activity would then be focused on the following main directions: - GCG and string theory. -New N(A)C geometries from string theory in non-constant back grounds and corresponding deformation of low energy dynamics. -Berkovits string and integrability in AdS/CFT.
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