Lectures related to Modular group

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Algorithms for Big Numbers: Z_n and Orders

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Representation of SL2Z

Delves into the representation of SL2Z and the function F, exploring its transformation properties and relation to modular forms.

Monster Group: Representation

Explores the Monster group, a sporadic simple group with a unique representation theory.

Modular Curves: Genus and Mapping Theorems

Explores holomorphic maps, ramification points, and the genus of a modular curve.

Extremal Lattices

Explores extremal lattices, emphasizing bounds on shortest vectors and unique modular forms.

Connect 4 Game Logic

Covers finalizing Connect 4 game logic, determining the winner, and handling tie situations.

Petersson Inner Product and Hecke Operators

Covers the Petersson inner product and Hecke operators in modular forms theory, exploring their definitions and properties.

Meromorphic Differentials and Modular Forms

Explores meromorphic differentials on Riemann surfaces and modular forms on congruence subgroups.

Prime Numbers: Deterministic Approaches

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

Dynamics on Homogeneous Spaces and Number Theory

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

Unit Tangent Bundle of Hyperbolic Spaces

Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.

Automorphism Groups: Essential Chief Series

Explores essential chief series in tdlc groups, focusing on closed, normal subgroups and their chief factors.

Number Theory: Modular Arithmetic

Explores modular arithmetic, congruence, and number manipulation in a mathematical context, showcasing the power of modular reduction and the tricks of casting out nines.

Fourier Expansion and Modular Forms

Covers the Fourier expansion of modular forms and the Rankin-Selberg method.

Modular Forms: Dimension Formulas

Covers dimension formulas for modular forms and related proofs using Riemann-Roch corollaries.

Macdonald identities

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Modular Lambda Function: Properties and Applications

Explores the modular lambda function, its properties, and applications in modular forms.

Canonical Divisors and Modular Forms

Covers canonical divisors on Riemann surfaces and properties of modular forms.

Prime Numbers and Algorithms

Covers prime numbers, primality testing algorithms, modular arithmetic, and efficient exponentiation methods.