Research objectives and content
The objective of this project is to understand the topological structure of the space of all rational curves on a toric variety. Every such variety admits a combinatorial description, and so does the space of rational curves on it.
One hopes to use this description to apply the homotopy theoretic machinery of iterated loop spaces.
Training content(objective,benefit and expected impact)
The Mathematical Institute in Oxford,where i am reading for D.Phil. Degree, hosts the geometry and the topology research groups. The activity of Donaldson,Kirwan,Steer,Tillmann in algebraic geometry,gauge theory, homotopy theory,is relevant to the project.