Ranks of points via Macaulay 2

Algebra Student Seminar
Friday, April 8, 2022 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006 or ONLINE
Jaewoo Jung – Georgia Tech – https://sites.google.com/view/ga-sas/
Marc Harkonen

The rank of a point $p$ with respect to a non-degenerate variety is the smallest number of the points in the variety that spans the point $p$. Studies about the ranks of points are interesting and important in various areas of applied mathematics and engineering in the sense that they are the shortest sizes of the decompositions of vectors into combinations of simple vectors.

In this talk, we focus on the ranks of points with respect to the rational normal curves, i.e. Waring ranks of binary forms. We introduce an algorithm that produces random points of given rank r. (Note that if we choose points randomly, we expect the rank of the points is just the generic rank.) Moreover, we check some known facts by Macaulay 2 computations. Lastly, we discuss the maximal and minimal rank of points in linear spaces.


Teams link: https://teams.microsoft.com/l/meetup-join/19%3a3a9d7f9d1fca4f5b991b4029b09c69a1%40thread.tacv2/1649360107625?context=%7b%22Tid%22%3a%22482198bb-ae7b-4b25-8b7a-6d7f32faa083%22%2c%22Oid%22%3a%2206706002-23ff-4989-8721-b078835bae91%22%7d