Lecture

Unit Tangent Bundle of Hyperbolic Spaces

Related lectures (28)

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

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

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

Covers the theory behind Gaussian processes and the design of receivers using MAP calculations.

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

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

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

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

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

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

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

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

Explores the discriminant's role in equations, symmetry, and orbits in mathematical spaces.

Explores fluid mechanics, hydrostatic equilibrium, and the chimney effect in tubes.

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

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

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

Explores the rheology of materials, drawing parallels between cats' behavior and material properties.

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