String theory has a very beautiful and rich mathematical structure. And yet the common feeling is that the theory in its current formulation is unsatisfactory and perhaps even misleading. What are the fundamental degrees of freedom? Is the string perturbation theory the right approach to quantizing gravity? And if it is, what is the correct definition of the quantum theory living on the string worldsheet?

In the last several years new exciting results were obtained in the theory on the string worldsheet. One important achievement is the discovery of the pure spinor formalism by N.J. Berkovits. It gives an effective method of calculations of the string theory amplitudes at higher genus. Another important achievement is the use of integrability in AdS/CFT correspondence.

My work is directed towards the fusion of these new approaches. Most importantly, the application of the pure spinor formalism to the study of the AdS/CFT correspondence may be crucial for understanding the very foundations of string theory.