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 ...
We propose an introduction to homotopy theory for topological spaces. We define higher homotopy groups and relate them to homology groups. We introduce (co)fibration sequences, loop spaces, and suspensions. We study long exact sequences. We construct Eilen ...
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 ...
The theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, topological algebraic geometry and twisted K-theory ...
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. ...
ln this course we will develop algebraic and coalgebraic models for homotopy types.
Among other things we will learn about Quillen's and Sullivan's model of rationâl homotopy types and about Mandell's theorem in p-adic homotopy theory. ...
We expect these mini-courses to equip junior researchers with new tools, techniques, and perspectives for attacking a broad range of questions in their own areas of research while also inspiring students to learn more about ground-breaking advances in pure ...
This course introduces the elementary topological concepts and tools that recently spread from condensed matter physics to various quantum and classical wave systems. ...
The goal of this course/seminar is to introduce the students to some contemporary aspects of geometric group theory. Emphasis will be put on Artin's Braid groups and Thompson's groups. ...