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 ...
We will survey state of the art research on quantum algebras that arise from quivers. Our guiding examples will be quantum loop groups associated to symmetric Cartan matrices, but we will also seek to understand the general theory, where many open results ...
The microstructure of many alloys and ceramics are constituted of very fine intricate domains (variants) created by diffusive or displacive phase transformations. The course introduces the crystallographic tools required to define, calculate and predict th ...
A decentralized system is one that works when no single party is in charge or fully trusted. This course teaches decentralized systems principles while guiding students through the engineering of their own decentralized system featuring messaging, file sha ...
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 ...
The aim of the course is to give an introduction to linear algebraic groups and to give an insight into a beautiful subject that combines algebraic geometry with group theory. ...
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, and topological algebraic geometry. ...
We will establish the major results in the representation theory of semisimple Lie algebras over the field of complex numbers, and that of the related algebraic groups. ...
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 ...