Nobuki Takayama (Kobe University, Japan)

Title: The Buchberger algorithm in the ring of differential operators
and its applications.

Abstract: The Buchberger algorithm for the ring of polynomials can be easily generalized to the ring of differential operators. However, 
during the past 10 years, we have seen that its applications are getting broader and more fruitful. 
I think that there are three main applications:
 (1) Applications to (commutative) algebraic geometry.
 (2) Applications to systems of hypergeometric equations.
 (3) Applications to study systems of linear partial differential equations.
This talk will be a survey about these applications.