MATH-512: Optimization on manifoldsWe develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
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-530: Differential geometry IV - general relativityThis course will serve as a basic introduction to the mathematical theory of general relativity. We will cover topics including the formalism of Lorentzian geometry, the formulation of the initial value problem for the Einstein equations and applications o ...
MATH-422: Introduction to riemannian geometryLa géométrie riemannienne est un (peut-être le) chapitre central de la géométrie différentielle et de la géométriec ontemporaine en général. Le sujet est très riche et ce cours est une modeste introduction aux bases du sujet. ...
MATH-322: Differential geometry II - smooth manifoldsSmooth manifolds constitute a certain class of topological spaces which locally look like some Euclidean space R^n and on which one can do calculus. We introduce the key concepts of this subject, such as vector fields, differential forms, etc. ...
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 ...
MATH-473: Complex manifoldsThe goal of this course is to help students learn the basic theory of complex manifolds and Hodge theory. ...
MATH-333: Selected chapters of geometryAprès avoir traité la théorie de base des courbes et surfaces dans le plan et l'espace euclidien,
nous étudierons certains chapitres choisis : surfaces minimales, surfaces à courbure moyenne constante,
caustiques, géométrie hyperbolique. ...
CS-455: Topics in theoretical computer scienceThe students gain an in-depth knowledge of several current and emerging areas of theoretical computer science. The course familiarizes them with advanced techniques, and develops an understanding of fundamental questions that underlie some of the key probl ...
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. ...
PHYS-431: Quantum field theory IThe goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...
MATH-731(2): Topics in geometric analysis IIThe goal of this course is to introduce the student to the basic notion of analysis on metric (measure) spaces, quasiconformal mappings, potential theory on metric spaces, etc. The subjects covered will vary each year. ...
MATH-731: Topics in geometric analysis IThe subject deals with differential geometry and its relation to global analysis, partial differential equations, geometric measure theory and variational principles to name a few. ...
MATH-605: Conformal bootstrap and Liouville conformal fieldThe course will focus on a probabilistic construction of a conformal field theory related to random Riemann surfaces, called the Liouville conformal field theory. The symmetries of the theory allow to express the n-point correlation functions in terms of 3 ...
