IntroductionThis course is devoted to the notion of magnitude homology and its relation to Euler characteristic of a finite category and GLMY-theory for digraphs. Tom Leinster in 2006 introduced a notion of Euler characteristic of a finite category, which is a rational number (not necessarily integer) that coincides with the Euler characteristic of the classifying space, when it is defined. Lat...
PrerequisiteThe course is designed to be essentially self-contained, but some background in higher-level mathematics is expected. Specifically, we need some basic results from Linear Algebra, Differential Equations, Complex Analysis, Group Theory, and elementary Algebraic Geometry.AbstractThis course is an introduction to some modern ideas of the geometric approach to two-dimensional discrete i...