Luis Daniel Abreu proves the (complex version of) the Monotonicity of Singular Values Conjecture

 

The semester is under way and, as I announced here, I am teaching a new version of the Mathematics of Data Science course I taught last fall. As I go through the material, and the open problems, I will announce here in the blog progress that has been done on the open problems since I last gave the class.

I am very happy to announce that Luis Daniel Abreu posted a proof for the complex version of the Conjecture regarding the Monotonicity of the average Singular Value of a Gaussian Matrix (see the Conjecture here: https://afonsobandeira.wordpress.com/2013/11/01/a-conjecture-on-the-singular-values-of-a-gaussian-matrix/ , it is Open Problem 1.2 of last years version of the class: http://www.cims.nyu.edu/~bandeira/Fall2015.18.S096.html )

Luis Daniel Abreu was a mentor of mine back in my undergraduate times, and was my first co-author! The solution is available in the arxiv at: http://arxiv.org/abs/1606.00494

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