Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...
This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...
Over the past decade, supply chain management has drawn enormous attention by industry and academia alike. Given an increasingly global economy, pronounced trends towards outsourcing and advances in information technology, more and more complex business re ...
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 ...
This course will explain the theory of vanishing cycles and perverse sheaves. We will see how the Hard Lefschetz theorem can be proved using perverse sheaves. If we have more time we will try to see the decomposition theorem and how to categorify certain p ...
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. ...
In this course we will describe in numerous examples how methods from l-adic cohomology as developed by Grothendieck, Deligne and Katz can interact with methods from analytic number theory (prime numbers, modular forms etc...). ...
This is a course about group schemes, with an emphasis on structural theorems for algebraic groups (e.g. Barsotti--Chevalley's theorem). All the basics will be covered towards the proof of such theorem, with an estress on the modern presentation using sche ...
This course presents geometric constructions of irreducible representations of semi-simple Lie Algebras and their Weyl groups by means of Springer theory. ...