Canonical Divisors and Modular Forms

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Related lectures (51)

Modular Forms: Dimension Formula

Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.

Modular curves: Riemann surfaces and transition maps

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

Modular Curves: Genus and Mapping Theorems

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

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Meromorphic Differentials and Modular Forms

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

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.

Modular Forms: Dimension Formulas

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

Theta functions: Properties and Transformations

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

Building surfaces from equilateral triangles

Explores the construction of Riemann surfaces from equilateral triangles and the dynamics of finite-type maps.

Fourier Expansion and Modular Forms

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

Automorphism Groups: Essential Chief Series

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

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Extremal Lattices

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Modular Lambda Function: Properties and Applications

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

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

E8 Lattice Optimality

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

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