Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group coho ...
This advanced theoretical course introduces students to basic concepts in wave scattering theory, with a focus on scattering matrix theory and its applications, in particular in photonics. ...
Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be m ...
This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in ...
This course introduces the elementary topological concepts and tools that recently spread from condensed matter physics to various quantum and classical wave systems. ...