MATH-563: Student seminar in pure mathematicsThe goal of the seminar is to learn the main aspects of class field theory, which aims at understanding abelian extensions of global fields in terms of the arithmetic of the field. The theory can also be seenas a first instance of the Langlands corresponde ...
MATH-726: Working group in Topology IThe 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. ...
MATH-436: Topology V.a - Homotopical algebraThis 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 ...
MATH-726(2): Working group in Topology IIThe 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 ...
MATH-410: Riemann surfacesThis 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 ...
MATH-328: Algebraic geometry I - CurvesAlgebraic 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. ...
MATH-535: Algebraic geometry III - selected topicsThis course is an introduction to intersection theory on algebraic varieties.
An important aim of the course is to develop geometric intuition while using the language of schemes developed in the basic algebraic geometry course, thus building a solid foun ...
MATH-473: Complex manifoldsThe goal of this course is to help students learn the basic theory of complex manifolds and Hodge theory. ...
MATH-225: Topologie II - groupes fondamentauxOn étudie des notions de topologie générale: unions et quotients d'espaces topologiques; on approfondit les notions de revêtements et de groupe fondamental,et d'attachements de cellules et on démontre le Théorème de Seifert-van Kampen. Des exemples de surf ...
MATH-479: Linear algebraic groupsThe 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. ...
MATH-667: Quivers and quantum algebrasWe 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 ...
MATH-658: Vanishing cycles and perverse sheavesThis 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 ...
MATH-657: Deformation TheoryWe will study classical and modern deformation theory of schemes and coherent sheaves. Participants should have a solid background in scheme-theory, for example being familiar with the first 3 chapters of Hartshorne's 'Algebraic Geometry'. ...
MATH-613: Abelian varietiesThis will be a basic course on abelian varieties. We will start with the analytic point of view, and then we will pass on to the algebraic one. A basic knowledge of differential geometry and algebraic geometry will be important to follow the course. ...
MATH-643: Applied l-adic cohomologyIn 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...). ...
MATH-645: Young Topologists Meeting Mini-CoursesWe 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 ...
