Explore a deep dive into lattice theory with this one-hour lecture on the Reverse Minkowski Theorem presented by Noah Stephens-Davidowitz from MIT. Delve into topics such as counting lattice points, determinants of lattices, and Minkowski's Theorem. Learn about applications in algorithms for Hermite SVP, Gaussian mass, and the space of stable lattices. Examine the proof process, from initial attempts to the final theorem, and consider open questions in the field. Gain insights into advanced concepts in geometry, algorithms, and computational hardness related to lattices.
Overview
Syllabus
A Reverse Minkowski Theorem
Counting Lattice Points: Pop Quiz!
Determinant of a Lattice
Minkowski's Theorem
Applications: Algorithms for Hermite SVP
Spoiler
Gaussian Mass
Space of (Stable) Lattices
Ct lies on the boundary
Dream Proof Fails
Slightly Less Dreamy Proof
Our Actual Proof
The Actual Theorem
Summary
Open Questions
Taught by
Simons Institute
