Concept

Congruence subgroup

This course introduces the basics of cryptography. We review several types of cryptographic primitives, when it is safe to use them and how to select the appropriate security parameters. We detail how

MATH-310: Algebra

This is an introduction to modern algebra: groups, rings and fields.

PHYS-702: Advanced Quantum Field Theory

The course builds on the course QFT1 and QFT2 and develops in parallel to the course on Gauge Theories and the SM.

MATH-113: Algebra I - fundamental structures

Le but de ce cours est d'introduire et d'étudier les notions de base de l'algèbre abstraite.

MATH-511: Number theory II.a - Modular forms

In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.

MATH-535: Algebraic geometry III - selected topics

This course is an introduction to the theory of algebraic curves and surfaces. An important aim of the course is to develop geometric intuition while using the language of schemes developed in the ba

MATH-620(2): Topics in the theory of reductive algebraic groups, Lie algebras, and representation theory II

The topics addressed in this course are the structure theory of reductive algebraic groups, their associated Lie algebras, the related finite groups of Lie type, and the representation theory of all o

MATH-620(1): Topics in the theory of reductive algebraic groups, Lie algebras, and representation theory I

MATH-680: Monstrous moonshine

The monstrous moonshine is an unexpected connection between the Monster group and modular functions. In the course we will explain the statement of the conjecture and study the main ideas and concepts

MATH-603: Subconvexity, Periods and Equidistribution

This course is a modern exposition of "Duke's Theorems" which describe the distribution of representations of large integers by a fixed ternary quadratic form. It will be the occasion to introduce the