**Date & Time:** Wednesday, March 12, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** S. M. Bhatwadekar, Bhaskaracharya Pratishthana

**Title:** Projective modules over the kernel of a locally nilpotent
derivation on an affine space

**Abstract:** Let $k$ be an algebraically closed field of characteristic
zero, $D$ be a locally
nilpotent derivation on the polynomial algebra $k[X_1, \cdots , X_n]$
and $A$ be the kernel of $D$. In this set up a question of Miyanishi
asks whether finitely generated projective modules over $A$ are free.
Note that for $n = 3$, by a result of Miyanishi, the kernel $A$ is a
polynomial algebra in two variables over $k$ and hence an answer to
the question is affirmative.
In my talk I will address this question for $n = 4$.