Oded Regev: The Reverse Minkowski Theorem

Explore the fascinating world of lattice theory in this 44-minute lecture by Oded Regev titled "The Reverse Minkowski Theorem." Delve into the history of lattices and their fundamental properties, including the concept of determinant as volume per lattice point. Examine Minkowski's Theorem and its potential converse, followed by an in-depth discussion on applications of the Reverse Minkowski Theorem. Investigate topics such as sphere packing, mixing time on flat tori, and the proof of the Reverse Minkowski Theorem through various cases. Conclude with a summary and ponder the main open question: Is Zn the "densest lattice"? This mathematical journey provides valuable insights into lattice theory and its implications in various fields of study.

Intro
Lattices
History
Determinant of a Lattice Determinant = volume per lattice point
Sphere Packing
Minkowski's Theorem
Converse?
Applications of Reverse Minkowski [DadushR16]
Mixing Time on Flat Tori
More Applications
Reverse Minkowski: Proof
Case 1: maximum on boundary
Case 2: maximum in interior
Bounding Local Maxima
Summary
Main open question: Is Zn the "densest lattice"?