**Date & Time:** Wednesday, March 09, 2016, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:**M.S. Raghunathan,

IIT Bombay

**Title:** Morphisms of affine curves into homogeneous
spaces

**Abstract:** Let X
be an affine curve G, a connected reductive algebraic group and H a
connected closed reductive algebraic subgroup. Assume that either the coordinate ring C[X]
is a unique factorization domain or that H is semisimple. Let M (X, G/H) be the set
of morphisms of X in G/H and C(X, G/H) the space of all continuous maps of X in
G/H equipped the topology of uniform convergence on compact sets where X and G/H
are given the Hausdorff topology. The set M (X, G/H) is in a natural fashion the inductive
limit of affine varieties and can be given the inductive limit of the Hausdorff topologies on
these varieties. Then the natural incusion of M (X, G/H) in C(X, G/H) is a homotopy
equivalence.