Extremal Lattices

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Related lectures (28)

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E8 Lattice Optimality

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Monster Group: Representation

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

Petersson Inner Product and Hecke Operators

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

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.

Meromorphic Differentials and Modular Forms

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

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.