Lectures related to Modular form

Automorphism Groups: Essential Chief Series

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

Modular Forms: Properties and Applications

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

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.

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.

Unit Tangent Bundle of Hyperbolic Spaces

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

Connect 4 Game Logic

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

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Pentagonal Number Theorem and Jacobi Identity

Covers the pentagonal number theorem, Jacobi identity, and modularity of eta and theta functions.

Macdonald identities

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

Monster Group: Representation

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

Canonical Divisors and Modular Forms

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

Representation of SL2Z

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

Lattices: Properties and Theta Functions

Explores lattices in Rd, Gram matrices, theta functions, and modular properties.

Architectural Realism: Lukács and Grassi

Delves into architectural realism, emphasizing the importance of adapting designs to their surroundings and achieving a harmonious blend of form and function.

E8 Lattice Optimality

Delves into the construction and optimality of the E8 lattice as the densest sphere packing in dimension eight.

Theta functions: Properties and Transformations

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

Homogeneous Hecke Sets: Equidistribution and Minimality

Explores the equidistribution of CM points in homogeneous Hecke sets.

Extremal Lattices

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