29 May 2008; Mat-Nat Faculty (UiT), room A228. Thursday 12:15-13:15

Sudhir Ghorpade (Indian Institute of Technology, Bombay, India)

"Geometry of subspaces of a Vector Space and Applications to Coding Theory".

Consider a finite dimensional vector space V over a field and the collection of all subspaces of V of a fixed dimension (Grassmannian). I will begin by explaining how this collection can be regarded as the locus of common zeros of a bunch of  homogeneous polynomials. Configurations such as these are basic objects of study in algebraic geometry and are known as projective algebraic varieties.

Next, we will touch upon some of the group-theoretic, topological and combinatorial aspects of the Grassmannians. Subsequently, I will outline a connection with the study of linear error correcting codes and related questions of current research interest. I will conclude with a brief summary of some of the known results and open problems on this topic.

Much of this talk will be expository in nature and, in particular, no formal background in algebraic geometry or coding theory will be assumed.