Minicourse 1: Laplacians, Jacobians, and Harmonic Automorphisms of Graphs
Lecturer: Alexander Mednykh, Sobolev Institute, University of Novosibirsk, Novosibirsk, Russia
This course will cover the following topics: The Laplacian matrix of a graphs and its eigenvalues, Spanning trees, Coverings of graphs and uniformization theory, Branched coverings of graphs, Jacobians of graphs, Harmonic automorphisms of graphs.
Lecturer: Eamonn O'Brien, University of Auckland, Auckland, New Zealand
This course will focus on theoretical and practical algorithms for the study of groups generated by matrices. Topics covered will include: Basic computations with matrix group, Strategies for the study of matrix groups defined over finite fields, Working with simple groups. The Soluble Radical model, Basic tasks for finitely-generated matrix groups over fields of characteristic 0.
According to regulations and in view of the amount of work designed for this courses, the Summer School is credited with 2 ECTS. In order to collect the assigned credit points, the student must solve a certain number of problems and tasks as required by the lecturer.