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A Reverse Minkowski Theorem
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Counting Lattice Points: Pop Quiz!
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Determinant of a Lattice
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Minkowski's Theorem
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Applications: Algorithms for Hermite SVP
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Spoiler
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Gaussian Mass
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Space of (Stable) Lattices
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Ct lies on the boundary
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Dream Proof Fails
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Slightly Less Dreamy Proof
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Our Actual Proof
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The Actual Theorem
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Summary
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Open Questions
Description:
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.

A Reverse Minkowski Theorem

Simons Institute
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