Lectures related to Representation of SL2Z

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

Modular Forms: Properties and Applications

Covers the properties and applications of modular forms and discusses equidistribution and modularity.

Theta functions: Properties and Transformations

Explores the properties and transformations of theta functions, including modular forms and lattice levels.

Petersson Inner Product and Hecke Operators

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

Macdonald identities

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

Closure Conversion: Representation and Transformation

Explores the representation and transformation of values, focusing on closure conversion and the challenges of representing functions in functional languages.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

General Fields: Lorentz Representations

Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

Canonical Divisors and Modular Forms

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

Jacobi Identity in Lie Algebra

Explores the significance of the Jacobi identity in Lie algebra and its impact on linear vector spaces.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Fourier Expansion and Modular Forms

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

Unit Tangent Bundle of Hyperbolic Spaces

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

Modular Forms: Dimension Formulas

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

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Lie Groups: Representations and Transformations

Explores Lie groups, scalar fields, and vector spaces transformations.

Representation of Lorentz Fields

Explains the representation of Lorentz fields and the concept of gravitons and gravitinos.

Meromorphic Differentials and Modular Forms

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

Extremal Lattices

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