MATH-670: The theta correspondenceIn the course we will discuss some introductory aspects of the local/global theta correspondence for automorphic forms/representation for various dual pairs. One of the objectives will be to prove Waldspurger's formula relating SO(2) periods to L-functions ...
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: 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 ...
FIN-414: Optimization methodsThis course presents the problem of static optimization, with and without (equality and inequality) constraints, both from the theoretical (optimality conditions) and methodological (algorithms) point of view. Economics and financial applications are provi ...
PHYS-331: Functional analysis (for PH)Ce cours ambitionne de présenter les mathématiques de la mécanique quantique, et plus généralement de la physique quantique. Il s'adresse essentiellement aux physiciens, ou a des mathématiciens intéressés dans le domaine. ...
MATH-687: Algebraic models for homotopy typesln 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. ...
MATH-494: Topics in arithmetic geometryP-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...
CS-233(a): Introduction to machine learning (BA3)Machine learning and data analysis are becoming increasingly central in many sciences and applications. In this course, fundamental principles and methods of machine learning will be introduced, analyzed and practically implemented. ...
MATH-495: Mathematical quantum mechanicsQuantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...
MATH-473: Complex manifoldsThe goal of this course is to help students learn the basic theory of complex manifolds and Hodge theory. ...
