# Minicourse: Deformations of path algebras of quivers with relations

The minicourse consists of 4 lectures.

**Dates**

**Tue 29/9 12-13 and 15-16Thu 1/10 10-11 and 13:30-14:30**

**Lecturers**

Severin Barmeier and Zhengfang Wang

**Abstract**

Path algebras of quivers with relations naturally occur throughout representation theory and algebraic geometry — for example in the representation theory of finite-dimensional algebras, as the coordinate ring of an affine variety, or as the endomorphism algebra of a tilting bundle.

In this minicourse we show how to give an explicit description of the deformation theory of these algebras for any finite quiver and any finitely generated ideal of relations. This description can be obtained by choosing a so-called reduction system, which can be used to describe all deformations of the algebra by giving a systematic method of deforming the relations.

Some of the related topics that we will discuss include: reduction systems and noncommutative Gröbner bases, deformation theory via L-infinity algebras, algebraization of formal deformations and deformation quantization of Poisson structures.

We aim to make the lectures accessible to non-experts and will include many examples.

**Video recordings**