String theory is the most promising candidate for a theory that would unify all of the known physical forces. It is also connected with other branches of theoretical physics and is associated with a rich interplay between physics and mathematics. In the past three years there has been great progress in our understanding of string theory. Using duality symmetries, we now know that all ten-dimensional supersymmetric string theories, which had hitherto been considered as different theories, and a new eleven dimensional theory, are all different limits of a single underlying structure called M-theory. In addition to strings, extended objects or 'p-branes' play a key role in M-theory. The key objectives of the proposal is to further understand the properties of M-theory, duality symmetries and the physics of branes.
One have learned that it is possible to obtain exact results about strongly coupled supersymmetric quantum field theories using branes in string theory. One realizes the supersymmetric field theory as the low-energy dynamics on various branes, or intersecting branes, and studies them in limits where the gravitational interactions can be neglected. The brane perspective provides us with a very powerful tool to study the moduli spaces of vacua of these theories and to elucidate duality relations. It seems that recent progress in obtaining exact results in field theory, following Seiberg and Witten's seminal work, have their origins in string theory and M-theory. There are many issues we would like to explore, such as for example, the construction of theories with exceptional gauge groups, including more general matter fields than has been done to date.

More concretely, in the project, it is supposed to study nonperturbative aspects of supersymmetric quantum field theories using branes in string theory; to formulate the renormalization group equations in supersymmetric gauge theories in terms of branes; to establish the interrelations between WDVV (associativity) equations, integrable systems and Whitham type hierarchies, especially in the context of the Seiberg-Witten solutions of supersymmetric theories; to further elucidate properties of the Matrix Theory conjecture of M-theory; to study connections of brane configurations with non-commutative geometry; to calculate quasiclassically the amplitude for pair creation of black holes in background fields within the D-brane approach; to determine correlators in N=1 and N=0
supersymmetric theories in terms of brane configurations in M- and F-theory; to study different solutions of self-duality equations in d=4 and Bogomolny equations in d=3 and the relation with amplitudes in Yang-Mills theory; to study self-dual Yang-Mills equations in $D\le 8$ and the connection to topological field theories and D-brane physics.