The Summerschool is intended for Ph.D. students and (early) postdocs.
The aim of this summer school is to understand and explore some of the modern techniques used in the study of coherent sheaves over weighted projective lines (in the sense of Geigle and Lenzing). In particular we will cover the associated Lie algebras, which are loop algebras of Kac-Moody Lie algebras, and a construction due to Peng and Xiao of Lie algebras from certain triangulated categories using Hall algebra methods. At the end we will combine these ideas and cover the proof by W. Crawley-Boevey of an analogue of Kac's Theorem for weighted projective lines. In addition, there will a couple of overview talks shedding light on further developments and applications of certain concepts.
The Summerschool will follow the tradition of previous spring/summerschools in representation theory. Every participant chooses a subject of the program (see below) and gives a talk.The typical participant will not be an expert in the subject, but working in one of the fields indicated above and interested in jointly learning a new subject. There will be no special prerequisities except for standard knowledge in representation theory, but participants are expected to prepare themselves and their talks in advance. It is recommended that this is done in small groups; in particular, the talks could/should be subdivided into smaller parts.
At the end of the week, there will be invited lectures by Helmut Lenzing.