Modular Curves: Genus and Mapping Theorems

Related lectures (30)

Page 3 of 3

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Covers the Lebesgue integration of simple functions and the approximation of nonnegative functions from below using piecewise constant functions.

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

Covers conformal blocks and their significance in complex structures and moduli spaces.

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

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores de Rham theory, L-values, and extensions, including special value formulas and examples related to Hecke characters and modular forms.