KOBE Summer School 2015

・Kobe - Lyon Summer School in Mathematics 2015
      On Quivers: Computational Aspects and Geometric Applications

      Date : July 21-31, 2015
      Venue : Graduate School of Science, Kobe University, Japan

The objective of the first week is to provide an introduction to Gröbner bases in the commutative and non-commutative aspect. Several applications will be presented, in particular to solve computational problems in the rings of differential operators and in homological algebra. We will expose the notion of Gröbner bases for several type of algebras such as associative algebras, Lie algebras and path algebras. We will give a description of the operations of integral transformation and restriction on modules over the rings of differential operators based on non-commutative Gröbner bases. We will present several methods allowing to compute projective resolutions using Gröbner bases. We will also show the relations between Gröbner bases theory and rewriting theory. The lectures of the first week do not need any prerequisite on Gröbner bases. The objective of the second week is to provide basic backgrounds of quivers and their application to other fields. As one of such applications, we will explain the geometry of moduli spaces of meromorphic connections on the projective line with (ir)regular singularities.