Quadratic Forms and Hermite Constant, Reduction Theory by Radhika Ganapathy

Explore quadratic forms, Hermite constants, and reduction theory in this comprehensive lecture on sphere packing. Delve into techniques for computing the densest possible lattice packing, examining the relationship between lattices and quadratic forms. Investigate Hermite constants, extreme lattices, and critical quality forms. Learn about lattice reduction theory, including Lagrange-Seeban-Menkouski reduction and its application to calculating delta for dimensions up to 8. Study perfect forms, weekly eutactic lattices, and the proof connecting extreme forms to perfect forms. Conclude with an overview of Voronoi's algorithm for obtaining a complete list of perfect forms, gaining valuable insights into this fundamental area of geometry and number theory.

Quadratic forms and Hermite constant, reduction theory
Overview of some of the techniques that go into the computation of the densest possible lattice packing
Dictionary between lattices and quadratic form
What the Hermite constant and extreme lattices?
Densest possible lattice packing corresponds to figuring out the critical quality forms
Goal of lattice reduction theory
Lagrange-Seeban-Menkouski reduction
Which allows the calculation of delta, star of s in for n less than or equal to 8
Perfect forms
About weekly eutactic
Proof that extreme forms and perfect
Voronois algorithm to obtain a complete list of perfect forms