Concept
Modular group
Related courses (9)
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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-417: Number theory II.b - selected topics
This year's topic is "Additive combinatorics and applications." We will introduce various methods from additive combinatorics, establish the sum-product theorem over finite fields and derive various a
MATH-489: Number theory II.c - Cryptography
The goal of the course is to introduce basic notions from public key cryptography (PKC) as well as basic number-theoretic methods and algorithms for cryptanalysis of protocols and schemes based on PKC
COM-102: Advanced information, computation, communication II
Text, sound, and images are examples of information sources stored in our computers and/or communicated over the Internet. How do we measure, compress, and protect the informatin they contain?
MATH-410: Riemann surfaces
This 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
MATH-643: Applied l-adic cohomology
In 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 numb
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-802: Optimization, interpolation and modular forms
This summer school will explore basic concepts as well as recent developments in optimization, interpolation, and modular forms. There will be short courses as well as several standalone lectures by i
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