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A Reverse Minkowski Theorem

Geometric functional analysis and applications November 13, 2017 - November 17, 2017

November 16, 2017 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Oded Regev (New York University, Courant Institute)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Minkowski's theorem

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

12-Regev

Abstract

Informally, Minkowski's first theorem states that lattices that are globally dense (have small determinant) are also locally dense (have lots of points in a small ball around the origin). This fundamental result dates back to 1891 and has a very wide range of applications.

 

I will present a proof of a reverse form of Minkowski's theorem, conjectured by Daniel Dadush in 2012, showing that locally dense lattices are also globally dense (in the appropriate sense).

 

The talk will be self contained and I will not assume any familiarity with lattices.

 

Based on joint papers with Daniel Dadush and Noah Stephens-Davidowitz.

Supplements
30099?type=thumb Regev Notes 3.93 MB application/pdf Download
Video/Audio Files

12-Regev

H.264 Video 12-Regev.mp4 293 MB video/mp4 rtsp://videos.msri.org/data/000/030/020/original/12-Regev.mp4 Download
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