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
I am teaching a Mathematics of Data Science PhD level course at NYU Courant this Fall, I’ll be posting new Open Problems in this blog! See more info here.
I am happy to announce that there is significant progress on Open Problem 9.2. of my notes, in this paper Bruce Hajek, Yihong Wu, and Jiaming Xu show that, indeed, for communities, the natural Semidefinite Program is suboptimal!
Congratulations to the three!
The lecture notes for the course I gave this semester are now available here. Thanks to all the readers that gave me comments and feedback on the notes! I am sure the notes still contain many typos, if you find one, or have any general feedback, please let me know!