MATH-323: Topology III - HomologyHomology 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 ...
MATH-506: Topology IV.a - Cohomology ringsSingular 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 ...
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-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-488: Topology IV.b - Algebraic K-theoryAlgebraic K-theory, which to any ring R associates a sequence of groups, can be viewed as a theory of linear algebra over an arbitrary ring. We will study in detail the first two of these groups and some of their applications to other areas of mathematics. ...
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 ...
PHYS-463: Computational quantum physicsThe numerical simulation of quantum systems plays a central role in modern physics. This course gives an introduction to key simulation approaches, through lectures and practical programming exercises. Simulation methods based both on classical and quantum ...
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-310: AlgebraThis is an introduction to modern algebra: groups, rings and fields. ...
AR-302(ah): Studio BA6 (Malterre-Barthes)How is architecture made? 'Revolutionize Construction' unpacks the political economy of construction, examining who commissions, finances, and builds, and interrogating architects' roles. It explores how these systems might be revolutionized to enable the ...
MATH-497: Topology IV.b - homotopy theoryWe 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 ...
MATH-436: 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-616: Numerical methods for random PDEs and uncertaintyThe course focuses on mathematical models based on PDEs with random parameters, and presents numerical techniques for forward uncertainty propagation, inverse uncertainty analysis in a Bayesian framework and optimal control under uncertainty. ...
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-684: Spectral sequencesThe goal of the course is to learn how to construct and calculate with spectral sequences. We will cover the construction and introductory computations of some common and famous spectral sequences. ...
